CoCalc Public Filesresearch / partitions / parts.sagews
Author: Nathan McNew
Description: Partitions
1+2

3
load('PartitionAvoidanceGF.py')

load('IntegerPartitionPatterns.py')

CountAll(6,14)

[1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70] [6] [1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 41, 48, 57] [5, 1] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [4, 2] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [4, 1, 1] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [3, 3] [1, 2, 3, 5, 7, 10, 13, 17, 20, 26, 29, 35, 39, 48] [3, 2, 1] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [3, 1, 1, 1] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [2, 2, 2] [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [2, 2, 1, 1] [1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 41, 48, 57] [2, 1, 1, 1, 1] [1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70] [1, 1, 1, 1, 1, 1]
Test([4,2],100)

['NE', 'E'] -(x^4 - x^3 + x)/(x^4 - 2*x^3 + 2*x - 1) [1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50, 57, 65, 73, 82, 91, 101, 111, 122, 133, 145, 157, 170, 183, 197, 211, 226, 241, 257, 273, 290, 307, 325, 343, 362, 381, 401, 421, 442, 463, 485, 507, 530, 553, 577, 601, 626, 651, 677, 703, 730, 757, 785, 813, 842, 871, 901, 931, 962, 993, 1025, 1057, 1090, 1123, 1157, 1191, 1226, 1261, 1297, 1333, 1370, 1407, 1445, 1483, 1522, 1561, 1601, 1641, 1682, 1723, 1765, 1807, 1850, 1893, 1937, 1981, 2026, 2071, 2117, 2163, 2210, 2257, 2305, 2353, 2402, 2451, 2501]
factor(x^4 - 2*x^3 + 2*x - 1)

(x + 1)*(x - 1)^3
Test([5,3,1],10)

['NE', 'E', 'NE']
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1044, in execute exec compile(block+'\n', '', 'single', flags=compile_flags) in namespace, locals File "", line 1, in <module> File "./PartitionAvoidanceGF.py", line 99, in Test F = GFTree(L,1) File "./PartitionAvoidanceGF.py", line 60, in GFTree F0 = GFTree(L[1:], 0) File "./PartitionAvoidanceGF.py", line 54, in GFTree G = (GFTree(L[1:],1) - x*t*GFTree(L[1:],x*t))/(1-x*t) File "./PartitionAvoidanceGF.py", line 60, in GFTree F0 = GFTree(L[1:], 0) File "./PartitionAvoidanceGF.py", line 70, in GFTree return x*t/(1-x*t) TypeError: unsupported operand type(s) for *: 'Partitions_n_with_category.element_class' and 'int'
for n in [1..1000]:
count=0
for a in [1..n]:
for b in [0..n-a]:
if b==0:
if a<n:
continue
if b%a==0 and a+b<n:
continue
r=b%a
c=n-a-b
#if c>0 and c%r==0:
#    continue
count+=1
#print (a,b,c)
print count,',',

1 , 2 , 3 , 5 , 7 , 11 , 14 , 20 , 25 , 32 , 39 , 49 , 56 , 68 , 79 , 91 , 103 , 119 , 132 , 150 , 165 , 183 , 202 , 224 , 241 , 264 , 287 , 311 , 334 , 362 , 385 , 415 , 442 , 472 , 503 , 535 , 563 , 599 , 634 , 670 , 703 , 743 , 778 , 820 , 859 , 899 , 942 , 988 , 1027 , 1074 , 1119 , 1167 , 1214 , 1266 , 1313 , 1365 , 1414 , 1468 , 1523 , 1581 , 1630 , 1690 , 1749 , 1807 , 1865 , 1927 , 1986 , 2052 , 2115 , 2181 , 2244 , 2314 , 2375 , 2447 , 2518 , 2588 , 2659 , 2733 , 2804 , 2882 , 2953 , 3030 , 3109 , 3191 , 3264 , 3346 , 3429 , 3513 , 3594 , 3682 , 3761 , 3849 , 3936 , 4026 , 4117 , 4209 , 4294 , 4390 , 4483 , 4577 , 4669 , 4769 , 4864 , 4966 , 5063 , 5161 , 5264 , 5370 , 5467 , 5575 , 5678 , 5786 , 5889 , 6001 , 6108 , 6220 , 6331 , 6443 , 6558 , 6674 , 6779 , 6898 , 7017 , 7137 , 7256 , 7378 , 7493 , 7619 , 7740 , 7866 , 7989 , 8119 , 8240 , 8370 , 8501 , 8629 , 8758 , 8894 , 9025 , 9163 , 9292 , 9430 , 9569 , 9709 , 9839 , 9981 , 10124 , 10266 , 10409 , 10557 , 10696 , 10846 , 10991 , 11139 , 11286 , 11438 , 11583 , 11739 , 11894 , 12050 , 12199 , 12357 , 12510 , 12672 , 12831 , 12989 , 13152 , 13318 , 13471 , 13638 , 13801 , 13967 , 14134 , 14306 , 14473 , 14643 , 14810 , 14984 , 15159 , 15337 , 15500 , 15680 , 15855 , 16035 , 16212 , 16394 , 16573 , 16757 , 16940 , 17122 , 17305 , 17495 , 17674 , 17866 , 18057 , 18245 , 18433 , 18629 , 18816 , 19014 , 19203 , 19401 , 19600 , 19800 , 19993 , 20195 , 20398 , 20600 , 20799 , 21005 , 21200 , 21410 , 21617 , 21827 , 22038 , 22250 , 22451 , 22665 , 22880 , 23096 , 23305 , 23523 , 23738 , 23960 , 24173 , 24390 , 24613 , 24839 , 25056 , 25284 , 25507 , 25731 , 25956 , 26188 , 26411 , 26643 , 26874 , 27108 , 27339 , 27577 , 27798 , 28038 , 28275 , 28513 , 28752 , 28992 , 29231 , 29475 , 29716 , 29962 , 30205 , 30455 , 30690 , 30940 , 31191 , 31439 , 31687 , 31943 , 32194 , 32450 , 32699 , 32955 , 33214 , 33476 , 33725 , 33987 , 34246 , 34510 , 34773 , 35041 , 35296 , 35566 , 35829 , 36095 , 36366 , 36636 , 36901 , 37177 , 37452 , 37726 , 37991 , 38271 , 38546 , 38828 , 39107 , 39385 , 39664 , 39948 , 40219 , 40506 , 40789 , 41077 , 41364 , 41656 , 41939 , 42231 , 42520 , 42810 , 43105 , 43401 , 43684 , 43982 , 44281 , 44581 , 44876 , 45178 , 45473 , 45779 , 46076 , 46382 , 46685 , 46995 , 47292 , 47604 , 47915 , 48219 , 48530 , 48846 , 49157 , 49473 , 49780 , 50098 , 50413 , 50733 , 51043 , 51363 , 51686 , 52010 , 52331 , 52657 , 52972 , 53302 , 53629 , 53957 , 54288 , 54620 , 54937 , 55273 , 55606 , 55942 , 56271 , 56609 , 56940 , 57280 , 57617 , 57955 , 58298 , 58644 , 58981 , 59329 , 59668 , 60012 , 60353 , 60705 , 61052 , 61404 , 61755 , 62105 , 62460 , 62818 , 63155 , 63514 , 63873 , 64231 , 64584 , 64946 , 65305 , 65671 , 66030 , 66394 , 66757 , 67125 , 67486 , 67858 , 68225 , 68593 , 68962 , 69336 , 69699 , 70077 , 70446 , 70824 , 71203 , 71585 , 71954 , 72332 , 72715 , 73097 , 73480 , 73868 , 74243 , 74631 , 75012 , 75402 , 75793 , 76185 , 76564 , 76960 , 77355 , 77747 , 78133 ,
Too many output messages: 257 (at most 256 per cell -- type 'smc?' to learn how to raise this limit): attempting to terminate...
GetAvoidanceSequence([5,3,1],20)

[1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 67, 83, 105, 127, 156, 185, 222, 259, 305]
GetAvoidanceSequence([4,3,1],25)

[1, 2, 3, 5, 7, 11, 15, 21, 28, 37, 46, 59, 72, 87, 104, 124, 144, 168, 192, 220, 250, 282, 314, 352, 391]
[len([]) for i in [1..26]]

[1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676]
for n in [1..26]:
count=0
for a in [1..n]:
for b in [0..n-a]:
if b>0 and b%a==0:
continue
r=b%a
c=n-a-b
if b>0 and c>0 and c%r==0:
continue
count+=1
print count,


1 2 4 5 8 9 13 15 20 22 30 32 41 44 57 58 74 75 95 97 117 117 147 144 176 172
def d(n):
if n==0:
return 1
return len(divisors(n))

def sigma(n):
return sum(divisors(n))

def abcd(n):
return sum([d(k)*d(n-k) for k in [1..n-1]])


trips = dict()
for x in GenAllAvoiding([4,2,1],18):
y= x.conjugate()
a= y[0]
b=0
c=0
for i in [1..len(y)-1]:
if y[i]==a:
b+=a
else:
b+=y[i]
break
for j in [i+1..len(y)-1]:
c+=y[j]
if tuple([a,b,c]) in trips:
print "Duplicate!"
trips[tuple([a,b,c])]=y
print x.conjugate(), a,b,c

[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 1 17 0 [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 1 15 [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 3 13 [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 1 14 [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 5 11 [4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 4 1 13 [2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 7 9 [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 4 11 [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 5 1 12 [2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] 2 9 7 [6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 6 1 11 [2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] 2 11 5 [3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 7 8 [4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 4 5 9 [7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 7 1 10 [2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] 2 13 3 [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 8 1 9 [2, 2, 2, 2, 2, 2, 2, 2, 1, 1] 2 15 1 [3, 3, 3, 3, 1, 1, 1, 1, 1, 1] 3 10 5 [5, 5, 1, 1, 1, 1, 1, 1, 1, 1] 5 6 7 [9, 1, 1, 1, 1, 1, 1, 1, 1, 1] 9 1 8 [2, 2, 2, 2, 2, 2, 2, 2, 2] 2 16 0 [3, 2, 2, 2, 2, 2, 2, 2, 1] 3 2 13 [4, 4, 4, 1, 1, 1, 1, 1, 1] 4 9 5 [10, 1, 1, 1, 1, 1, 1, 1, 1] 10 1 7 [3, 3, 2, 2, 2, 2, 2, 2] 3 5 10 [4, 2, 2, 2, 2, 2, 2, 2] 4 2 12 [3, 3, 3, 2, 2, 2, 2, 1] 3 8 7 [5, 2, 2, 2, 2, 2, 2, 1] 5 2 11 [3, 3, 3, 3, 3, 1, 1, 1] 3 13 2 [6, 6, 1, 1, 1, 1, 1, 1] 6 7 5 [11, 1, 1, 1, 1, 1, 1, 1] 11 1 6 [3, 3, 3, 3, 2, 2, 2] 3 11 4 [4, 4, 2, 2, 2, 2, 2] 4 6 8 [6, 2, 2, 2, 2, 2, 2] 6 2 10 [3, 3, 3, 3, 3, 2, 1] 3 14 1 [7, 2, 2, 2, 2, 2, 1] 7 2 9 [12, 1, 1, 1, 1, 1, 1] 12 1 5 [3, 3, 3, 3, 3, 3] 3 15 0 [4, 3, 3, 3, 3, 2] 4 3 11 [4, 4, 4, 2, 2, 2] 4 10 4 [5, 5, 2, 2, 2, 2] 5 7 6 [8, 2, 2, 2, 2, 2] 8 2 8 [4, 4, 3, 3, 3, 1] 4 7 7 [5, 3, 3, 3, 3, 1] 5 3 10 [9, 2, 2, 2, 2, 1] 9 2 7 [4, 4, 4, 4, 1, 1] 4 13 1 [5, 5, 5, 1, 1, 1] 5 11 2 [7, 7, 1, 1, 1, 1] 7 8 3 [13, 1, 1, 1, 1, 1] 13 1 4 [4, 4, 4, 3, 3] 4 11 3 [6, 3, 3, 3, 3] 6 3 9 [4, 4, 4, 4, 2] 4 14 0 [5, 5, 3, 3, 2] 5 8 5 [7, 3, 3, 3, 2] 7 3 8 [6, 6, 2, 2, 2] 6 8 4 [10, 2, 2, 2, 2] 10 2 6 [5, 4, 4, 4, 1] 5 4 9 [8, 3, 3, 3, 1] 8 3 7 [5, 5, 5, 2, 1] 5 12 1 [11, 2, 2, 2, 1] 11 2 5 [14, 1, 1, 1, 1] 14 1 3 [5, 5, 4, 4] 5 9 4 [6, 4, 4, 4] 6 4 8 [5, 5, 5, 3] 5 13 0 [7, 4, 4, 3] 7 4 7 [6, 6, 3, 3] 6 9 3 [9, 3, 3, 3] 9 3 6 [6, 5, 5, 2] 6 5 7 [6, 6, 4, 2] 6 10 2 [8, 4, 4, 2] 8 4 6 [10, 3, 3, 2] 10 3 5 [7, 7, 2, 2] 7 9 2 [12, 2, 2, 2] 12 2 4 [6, 6, 5, 1] 6 11 1 [7, 5, 5, 1] 7 5 6 [9, 4, 4, 1] 9 4 5 [7, 7, 3, 1] 7 10 1 [11, 3, 3, 1] 11 3 4 [13, 2, 2, 1] 13 2 3 [8, 8, 1, 1] 8 9 1 [15, 1, 1, 1] 15 1 2 [6, 6, 6] 6 12 0 [7, 6, 5] 7 6 5 [8, 5, 5] 8 5 5 [7, 7, 4] 7 11 0 [8, 6, 4] 8 6 4 [9, 5, 4] 9 5 4 [10, 4, 4] 10 4 4 [8, 7, 3] 8 7 3 [9, 6, 3] 9 6 3 [10, 5, 3] 10 5 3 [11, 4, 3] 11 4 3 [12, 3, 3] 12 3 3 [8, 8, 2] 8 10 0 [9, 7, 2] 9 7 2 [10, 6, 2] 10 6 2 [11, 5, 2] 11 5 2 [12, 4, 2] 12 4 2 [13, 3, 2] 13 3 2 [14, 2, 2] 14 2 2 [9, 8, 1] 9 8 1 [10, 7, 1] 10 7 1 [11, 6, 1] 11 6 1 [12, 5, 1] 12 5 1 [13, 4, 1] 13 4 1 [14, 3, 1] 14 3 1 [15, 2, 1] 15 2 1 [16, 1, 1] 16 1 1 [9, 9] 9 9 0 [10, 8] 10 8 0 [11, 7] 11 7 0 [12, 6] 12 6 0 [13, 5] 13 5 0 [14, 4] 14 4 0 [15, 3] 15 3 0 [16, 2] 16 2 0 [17, 1] 17 1 0 [18] 18 0 0
for i in [1..10]:
abcd(i)

0 1 4 8 14 20 28 37 44 58
(abcd(3)+sigma(3))/2

6
def p321(n):
count=0
for d in [1..n]:
for c in [1..floor(n/d)]:
if c*d==n:
count+=1
else:
count+=len([i for i in divisors(n-c*d) if i<d])
return count

p321(12)

35
total=0
for i in [1..1000]:
c=p321(i)
total+=c
print i,c,total

1 1 1 2 2 3 3 3 6 4 5 11 5 7 18 6 10 28 7 13 41 8 17 58 9 20 78 10 26 104 11 29 133 12 35 168 13 39 207 14 48 255 15 48 303 16 60 363 17 61 424 18 74 498 19 73 571 20 87 658 21 86 744 22 106 850 23 99 949 24 120 1069 25 112 1181 26 140 1321 27 130 1451 28 155 1606 29 143 1749 30 176 1925 31 159 2084 32 194 2278 33 180 2458 34 216 2674 35 186 2860 36 240 3100 37 209 3309 38 258 3567 39 234 3801 40 274 4075 41 243 4318 42 308 4626 43 261 4887 44 325 5212 45 289 5501 46 348 5849 47 297 6146 48 383 6529 49 314 6843 50 392 7235 51 356 7591 52 423 8014 53 355 8369 54 460 8829 55 372 9201 56 468 9669 57 422 10091 58 496 10587 59 415 11002 60 548 11550 61 437 11987 62 548 12535 63 481 13016 64 579 13595 65 478 14073 66 632 14705 67 501 15206 68 639 15845 69 560 16405 70 648 17053 71 543 17596 72 727 18323 73 567 18890 74 714 19604 75 635 20239 76 757 20996 77 602 21598 78 816 22414 79 633 23047 80 811 23858 81 707 24565 82 830 25395 83 679 26074 84 926 27000 85 708 27708 86 890 28598 87 788 29386 88 932 30318 89 749 31067 90 1010 32077 91 768 32845 92 1009 33854 93 870 34724 94 1012 35736 95 828 36564 96 1136 37700 97 847 38547 98 1068 39615 99 941 40556 100 1144 41700 101 897 42597 102 1224 43821 103 921 44742 104 1196 45938 105 1042 46980 106 1204 48184 107 971 49155 108 1358 50513 109 997 51510 110 1272 52782 111 1122 53904 112 1331 55235 113 1049 56284 114 1444 57728 115 1090 58818 116 1415 60233 117 1197 61430 118 1402 62832 119 1120 63952 120 1602 65554 121 1150 66704 122 1474 68178 123 1300 69478 124 1557 71035 125 1226 72261 126 1656 73917 127 1233 75150 128 1623 76773 129 1390 78163 130 1622 79785 131 1285 81070 132 1836 82906 133 1312 84218 134 1682 85900 135 1498 87398 136 1774 89172 137 1369 90541 138 1908 92449 139 1395 93844 140 1870 95714 141 1576 97290 142 1824 99114 143 1436 100550 144 2077 102627 145 1514 104141 146 1900 106041 147 1673 107714 148 2009 109723 149 1535 111258 150 2174 113432 151 1563 114995 152 2080 117075 153 1757 118832 154 2032 120864 155 1660 122524 156 2350 124874 157 1651 126525 158 2120 128645 159 1864 130509 160 2268 132777 161 1710 134487 162 2398 136885 163 1737 138622 164 2325 140947 165 1994 142941 166 2270 145211 167 1791 147002 168 2616 149618 169 1818 151436 170 2384 153820 171 2059 155879 172 2489 158368 173 1883 160251 174 2664 162915 175 1969 164884 176 2551 167435 177 2168 169603 178 2500 172103 179 1969 174072 180 2925 176997 181 2003 179000 182 2576 181576 183 2270 183846 184 2736 186582 185 2120 188702 186 2932 191634 187 2076 193710 188 2819 196529 189 2374 198903 190 2788 201691 191 2153 203844 192 3175 207019 193 2185 209204 194 2818 212022 195 2526 214548 196 2992 217540 197 2245 219785 198 3182 222967 199 2277 225244 200 3135 228379 201 2586 230965 202 2982 233947 203 2350 236297 204 3464 239761 205 2440 242201 206 3060 245261 207 2683 247944 208 3231 251175 209 2416 253591 210 3548 257139 211 2467 259606 212 3339 262945 213 2800 265745 214 3226 268971 215 2602 271573 216 3760 275333 217 2576 277909 218 3310 281219 219 2906 284125 220 3572 287697 221 2602 290299 222 3764 294063 223 2651 296714 224 3610 300324 225 3095 303419 226 3480 306899 227 2717 309616 228 4062 313678 229 2749 316427 230 3644 320071 231 3138 323209 232 3788 326997 233 2815 329812 234 4032 333844 235 2942 336786 236 3871 340657 237 3238 343895 238 3736 347631 239 2907 350538 240 4454 354992 241 2945 357937 242 3810 361747 243 3353 365100 244 4057 369157 245 3141 372298 246 4348 376646 247 3022 379668 248 4156 383824 249 3464 387288 250 4090 391378 251 3103 394481 252 4695 399176 253 3130 402306 254 4080 406386 255 3676 410062 256 4338 414400 257 3207 417607 258 4644 422251 259 3274 425525 260 4518 430043 261 3699 433742 262 4254 437996 263 3305 441301 264 5004 446305 265 3464 449769 266 4360 454129 267 3812 457941 268 4613 462554 269 3403 465957 270 5052 471009 271 3439 474448 272 4709 479157 273 3950 483107 274 4522 487629 275 3631 491260 276 5328 496588 277 3543 500131 278 4610 504741 279 4049 508790 280 5074 513864 281 3613 517477 282 5256 522733 283 3643 526376 284 4993 531369 285 4280 535649 286 4760 540409 287 3756 544165 288 5662 549827 289 3742 553569 290 5030 558599 291 4286 562885 292 5193 568078 293 3815 571893 294 5594 577487 295 4000 581487 296 5310 586797 297 4402 591199 298 5062 596261 299 3900 600161 300 6119 606280 301 4010 610290 302 5156 615446 303 4524 619970 304 5487 625457 305 4184 629641 306 5872 635513 307 4059 639572 308 5610 645182 309 4646 649828 310 5508 655336 311 4127 659463 312 6340 665803 313 4165 669968 314 5436 675404 315 4984 680388 316 5783 686171 317 4233 690404 318 6200 696604 319 4260 700864 320 6065 706929 321 4888 711817 322 5660 717477 323 4320 721797 324 6671 728468 325 4545 733013 326 5718 738731 327 5014 743745 328 6116 749861 329 4512 754373 330 6688 761061 331 4487 765548 332 6183 771731 333 5151 776882 334 5900 782782 335 4742 787524 336 7072 794596 337 4591 799187 338 5984 805171 339 5260 810431 340 6564 816995 341 4658 821653 342 6854 828507 343 4770 833277 344 6532 839809 345 5568 845377 346 6192 851569 347 4769 856338 348 7360 863698 349 4803 868501 350 6552 875053 351 5518 880571 352 6714 887285 353 4883 892168 354 7188 899356 355 5128 904484 356 6795 911279 357 5690 916969 358 6474 923443 359 4983 928426 360 7964 936390 361 5018 941408 362 6578 947986 363 5767 953753 364 7056 960809 365 5324 966133 366 7524 973657 367 5137 978794 368 7133 985927 369 5919 991846 370 7008 998854 371 5290 1004144 372 8074 1012218 373 5245 1017463 374 6840 1024303 375 6232 1030535 376 7368 1037903 377 5306 1043209 378 7932 1051141 379 5359 1056500 380 7656 1064156 381 6154 1070310 382 7068 1077378 383 5429 1082807 384 8468 1091275 385 5806 1097081 386 7168 1104249 387 6311 1110560 388 7633 1118193 389 5541 1123734 390 8428 1132162 391 5554 1137716 392 7879 1145595 393 6412 1152007 394 7362 1159369 395 5908 1165277 396 8813 1174090 397 5691 1179781 398 7464 1187245 399 6614 1193859 400 8259 1202118 401 5769 1207887 402 8548 1216435 403 5794 1222229 404 8061 1230290 405 6955 1237245 406 7748 1244993 407 5886 1250879 408 9212 1260091 409 5925 1266016 410 8054 1274070 411 6808 1280878 412 8275 1289153 413 6096 1295249 414 8900 1304149 415 6310 1310459 416 8416 1318875 417 6934 1325809 418 7944 1333753 419 6105 1339858 420 9902 1349760 421 6151 1355911 422 8074 1363985 423 7113 1371098 424 8680 1379778 425 6487 1386265 426 9248 1395513 427 6372 1401885 428 8711 1410596 429 7198 1417794 430 8584 1426378 431 6333 1432711 432 9988 1442699 433 6377 1449076 434 8476 1457552 435 7624 1465176 436 8933 1474109 437 6426 1480535 438 9596 1490131 439 6487 1496618 440 9432 1506050 441 7631 1513681 442 8546 1522227 443 6573 1528800 444 10302 1539102 445 6924 1546026 446 8680 1554706 447 7604 1562310 448 9429 1571739 449 6685 1578424 450 10308 1588732 451 6736 1595468 452 9379 1604847 453 7742 1612589 454 8886 1621475 455 7246 1628721 456 10736 1639457 457 6841 1646298 458 8988 1655286 459 7902 1663188 460 9930 1673118 461 6917 1680035 462 10424 1690459 463 6959 1697418 464 9775 1707193 465 8340 1715533 466 9202 1724735 467 7035 1731770 468 11093 1742863 469 7214 1750077 470 9684 1759761 471 8154 1767915 472 10024 1777939 473 7164 1785103 474 10676 1795779 475 7511 1803290 476 10148 1813438 477 8347 1821785 478 9508 1831293 479 7265 1838558 480 11876 1850434 481 7308 1857742 482 9622 1867364 483 8552 1875916 484 10278 1886194 485 7756 1893950 486 11082 1905032 487 7431 1912463 488 10482 1922945 489 8566 1931511 490 10374 1941885 491 7505 1949390 492 11848 1961238 493 7522 1968760 494 9900 1978660 495 9150 1987810 496 10697 1998507 497 7786 2006293 498 11412 2017705 499 7671 2025376 500 11118 2036494 501 8844 2045338 502 10142 2055480 503 7741 2063221 504 12506 2075727 505 8178 2083905 506 10252 2094157 507 8985 2103142 508 10959 2114101 509 7865 2121966 510 12184 2134150 511 8072 2142222 512 11164 2153386 513 9170 2162556 514 10472 2173028 515 8390 2181418 516 12642 2194060 517 8046 2202106 518 10736 2212842 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3515981 632 14808 3530789 633 12034 3542823 634 13782 3556605 635 11030 3567635 636 16768 3584403 637 10769 3595172 638 13908 3609080 639 12291 3621371 640 15658 3637029 641 10593 3647622 642 16020 3663642 643 10631 3674273 644 15222 3689495 645 12896 3702391 646 14076 3716467 647 10715 3727182 648 17437 3744619 649 10822 3755441 650 14902 3770343 651 12708 3783051 652 15257 3798308 653 10853 3809161 654 16424 3825585 655 11484 3837069 656 15539 3852608 657 12741 3865349 658 14736 3880085 659 10971 3891056 660 18302 3909358 661 11021 3920379 662 14586 3934965 663 12770 3947735 664 15804 3963539 665 11962 3975501 666 16930 3992431 667 11114 4003545 668 15741 4019286 669 12922 4032208 670 15512 4047720 671 11288 4059008 672 18450 4077458 673 11279 4088737 674 14928 4103665 675 13804 4117469 676 15994 4133463 677 11365 4144828 678 17224 4162052 679 11688 4173740 680 16988 4190728 681 13232 4203960 682 15184 4219144 683 11493 4230637 684 18579 4249216 685 12176 4261392 686 15572 4276964 687 13382 4290346 688 16555 4306901 689 11638 4318539 690 18340 4336879 691 11665 4348544 692 16491 4365035 693 13996 4379031 694 15502 4394533 695 12404 4406937 696 19092 4426029 697 11778 4437807 698 15614 4453421 699 13680 4467101 700 17743 4484844 701 11877 4496721 702 18152 4514873 703 11904 4526777 704 17107 4543884 705 14516 4558400 706 15866 4574266 707 12320 4586586 708 19368 4605954 709 12059 4618013 710 16752 4634765 711 14135 4648900 712 17330 4666230 713 12102 4678332 714 18716 4697048 715 12970 4710018 716 17241 4727259 717 14144 4741403 718 16200 4757603 719 12263 4769866 720 20879 4790745 721 12636 4803381 722 16306 4819687 723 14302 4833989 724 17499 4851488 725 13069 4864557 726 18898 4883455 727 12445 4895900 728 18174 4914074 729 14594 4928668 730 17382 4946050 731 12524 4958574 732 20250 4978824 733 12577 4991401 734 16676 5008077 735 15620 5023697 736 18060 5041757 737 12750 5054507 738 19410 5073917 739 12713 5086630 740 18816 5105446 741 14774 5120220 742 17256 5137476 743 12805 5150281 744 20884 5171165 745 13580 5184745 746 17030 5201775 747 15079 5216854 748 18288 5235142 749 13270 5248412 750 20504 5268916 751 12975 5281891 752 18619 5300510 753 15072 5315582 754 17262 5332844 755 13808 5346652 756 21582 5368234 757 13111 5381345 758 17394 5398739 759 15278 5414017 760 19724 5433741 761 13201 5446942 762 20108 5467050 763 13590 5480640 764 18775 5499415 765 16314 5515729 766 17628 5533357 767 13358 5546715 768 21791 5568506 769 13377 5581883 770 19064 5600947 771 15548 5616495 772 19035 5635530 773 13461 5648991 774 20674 5669665 775 14247 5683912 776 19408 5703320 777 16024 5719344 778 17976 5737320 779 13568 5750888 780 22926 5773814 781 13734 5787548 782 18060 5805608 783 16012 5821620 784 20051 5841671 785 14538 5856209 786 20948 5877157 787 13781 5890938 788 19549 5910487 789 16016 5926503 790 19272 5945775 791 14230 5960005 792 22938 5982943 793 13952 5996895 794 18464 6015359 795 16996 6032355 796 19807 6052162 797 13993 6066155 798 21704 6087859 799 14036 6101895 800 21096 6122991 801 16525 6139516 802 18708 6158224 803 14232 6172456 804 22942 6195398 805 15354 6210752 806 18832 6229584 807 16492 6246076 808 20466 6266542 809 14265 6280807 810 22906 6303713 811 14311 6318024 812 20710 6338734 813 16646 6355380 814 19136 6374516 815 15246 6389762 816 23632 6413394 817 14430 6427824 818 19200 6447024 819 17418 6464442 820 21568 6486010 821 14543 6500553 822 22216 6522769 823 14585 6537354 824 21004 6558358 825 17902 6576260 826 19856 6596116 827 14675 6610791 828 24005 6634796 829 14721 6649517 830 20564 6670081 831 17126 6687207 832 21281 6708488 833 15207 6723695 834 22632 6746327 835 15730 6762057 836 21168 6783225 837 17456 6800681 838 19794 6820475 839 14941 6835416 840 25972 6861388 841 14986 6876374 842 19932 6896306 843 17452 6913758 844 21387 6935145 845 16027 6951172 846 23264 6974436 847 15655 6990091 848 21819 7011910 849 17610 7029520 850 21174 7050694 851 15184 7065878 852 24780 7090658 853 15265 7105923 854 20736 7126659 855 18890 7145549 856 22080 7167629 857 15357 7182986 858 23584 7206570 859 15399 7221969 860 22962 7244931 861 18336 7263267 862 20528 7283795 863 15489 7299284 864 25686 7324970 865 16468 7341438 866 20658 7362096 867 18091 7380187 868 22608 7402795 869 15744 7418539 870 25008 7443547 871 15734 7459281 872 22626 7481907 873 18485 7500392 874 20852 7521244 875 17114 7538358 876 25710 7564068 877 15815 7579883 878 21020 7600903 879 18412 7619315 880 24078 7643393 881 15901 7659294 882 25040 7684334 883 15955 7700289 884 22734 7723023 885 19560 7742583 886 21286 7763869 887 16037 7779906 888 26464 7806370 889 16542 7822912 890 22534 7845446 891 19055 7864501 892 22981 7887482 893 16158 7903640 894 24788 7928428 895 17196 7945624 896 23900 7969524 897 18926 7988450 898 21640 8010090 899 16282 8026372 900 27971 8054343 901 16372 8070715 902 21876 8092591 903 19520 8112111 904 23726 8135837 905 17464 8153301 906 25236 8178537 907 16507 8195044 908 23513 8218557 909 19473 8238030 910 23724 8261754 911 16599 8278353 912 27410 8305763 913 16776 8322539 914 22146 8344685 915 20428 8365113 916 23781 8388894 917 17212 8406106 918 25864 8431970 919 16779 8448749 920 25408 8474157 921 19558 8493715 922 22388 8516103 923 16938 8533041 924 28154 8561195 925 17909 8579104 926 22524 8601628 927 19979 8621607 928 24520 8646127 929 17015 8663142 930 27324 8690466 931 17539 8708005 932 24333 8732338 933 19888 8752226 934 22766 8774992 935 18330 8793322 936 28666 8821988 937 17201 8839189 938 23444 8862633 939 20058 8882691 940 25826 8908517 941 17291 8925808 942 26552 8952360 943 17302 8969662 944 25105 8994767 945 22004 9016771 946 23256 9040027 947 17437 9057464 948 28538 9086002 949 17556 9103558 950 24478 9128036 951 20384 9148420 952 25896 9174316 953 17577 9191893 954 27256 9219149 955 18704 9237853 956 25141 9262994 957 20646 9283640 958 23520 9307160 959 18222 9325382 960 30618 9356000 961 17752 9373752 962 23688 9397440 963 20991 9418431 964 25423 9443854 965 18950 9462804 966 27960 9490764 967 17903 9508667 968 26051 9534718 969 20878 9555596 970 25214 9580810 971 17995 9598805 972 29733 9628538 973 18576 9647114 974 24032 9671146 975 22236 9693382 976 26229 9719611 977 18139 9737750 978 27884 9765634 979 18330 9783964 980 27817 9811781 981 21503 9833284 982 24278 9857562 983
Too many output messages: 257 (at most 256 per cell -- type 'smc?' to learn how to raise this limit): attempting to terminate...