CoCalc Public FilesPossible counter examples to the p-adic Littlewood.sagewsOpen in CoCalc with one click!
Author: Erez Nesharim
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def Dragon(n): """ This function returns the nth element of the dragon sequence """ if n == 0: return 0 else: while Mod(n, 2) == 0: #while n%2 == 0: n = n / 2 return ((n-1)/2)%2 def Pagoda(n): """ This function returns the nth element of the pagoda sequence """ return Dragon(n+1) - Dragon(n-1) def seqToReal(seq,base=3): leng = len(seq) s = 0 oneOverBase = 1/base for i in range(0,leng): s += seq[i]*oneOverBase^i return s print() leng = 10000 base = 3 pag = [Pagoda(n) for n in range (0,leng)] pagBase = [Integer(Mod(pag[n],base)) for n in range (0,leng)] pagNumber = seqToReal(pagBase,base) print(pagNumber) print(pagNumber.continued_fraction())
() 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2, 36, 2, 1, 21, 5, 1, 1, 4, 1, 5, 3, 9, 1, 1, 2, 4, 1, 2, 6, 2, 5, 1, 1, 3, 1, 2, 43, 45, 12, 18, 12, 349, 2, 1, 5, 1, 2, 1, 1, 1, 30, 4, 1, 6, 24, 2, 26, 1, 2, 1, 2, 1, 1, 1, 1, 111, 2, 43, 2, 4, 2, 1, 2, 1, 9, 2, 4, 4, 1, 87, 1, 8, 1, 2, 3, 5, 1, 106, 4, 3, 1, 7, 2, 1, 3, 4, 2, 1, 6, 2, 1, 1, 5, 2, 1, 1, 1, 1, 35, 2, 1, 2, 1, 1, 3, 20, 17, 2, 3, 1, 1, 2, 10, 5, 1, 1, 5, 1, 2, 21, 56, 1, 1, 1, 9, 6, 2, 1, 1, 1, 134, 4, 4, 3, 11, 2, 3, 1, 5, 3, 1, 1, 1, 1, 2, 7, 1, 1, 3, 1, 3, 8, 1, 31, 4, 2, 8, 11, 4, 2, 17, 1, 1, 2, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2, 6, 2, 37, 1, 16, 6, 1, 17, 1, 1, 2, 1, 1, 7, 4, 3, 1, 1, 3, 2, 1, 2, 1, 1, 5, 1, 1, 5, 1, 2, 2, 13, 3, 2, 1, 9, 1, 1, 97, 1, 17, 59, 1, 1, 1, 1, 8, 3, 1, 1, 6, 2, 2, 1, 1, 7, 1, 10, 1, 1, 1, 6, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 10, 1, 31, 4, 2, 16, 43, 3, 2, 1, 2, 1, 3, 26, 2, 1, 28, 3, 2, 1, 1, 1, 10, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 2, 2, 3, 18, 2, 1, 4, 7, 3, 3, 1, 2, 4, 1, 3, 10, 1, 9, 1, 8, 1, 5, 1, 132, 1, 4, 2, 1, 6, 1, 1, 4, 2, 1, 1, 1, 23, 14, 1, 1, 1, 3, 20, 1, 6, 12, 1, 2, 1, 1, 12, 1, 2, 10, 4, 1, 10, 1, 1, 4, 1, 1, 210, 1, 5, 2, 1, 2, 1, 1, 3, 1, 6, 1, 3, 2, 1, 3, 8, 1, 1, 4, 8, 934, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 14, 2, 1, 5, 4, 5, 1, 9, 3, 1, 14, 1, 1, 5, 11, 3, 1, 13, 1, 1, 4, 1, 1, 6, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 3, 4, 1, 3, 1, 1, 5, 6, 2, 1, 1, 3, 1, 1, 2, 21, 9, 1, 1, 11, 1, 99, 81, 1, 4, 2, 2, 1, 2, 7, 1, 1, 1, 1, 4, 14, 1, 5, 2, 2, 1, 2, 6, 29, 12, 1, 1, 2, 2837, 1, 9, 7, 1, 2, 1, 2, 1, 3, 11, 1, 1, 1, 1, 1, 4, 37, 2, 1, 28, 1, 12, 1, 3, 1, 10, 1, 3, 1, 1, 1, 1, 5, 1, 6, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 4, 1, 4, 2, 2, 1, 62, 4, 10, 2, 1, 27, 1, 2, 7, 1, 2, 12, 1, 1, 5, 3, 1, 1, 18, 2, 1, 2, 2, 4, 2, 1, 2, 1, 1, 1, 2, 9, 13, 10, 1, 3, 2, 1, 42, 2, 4, 1, 5, 1, 5, 1, 1, 5, 9, 11, 4, 5, 3, 3, 4, 1, 1, 17, 1, 19, 2, 2, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 5, 6, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 2, 6, 1, 4, 4, 137, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 22, 48, 1, 1, 1, 149, 3, 57, 1, 1, 11, 3, 5, 2, 1, 6, 1, 4, 9, 3, 18, 1, 2, 1, 5, 2, 1, 7, 2, 47, 1, 2, 23, 11, 1, 2, 2, 22, 3, 81, 1, 1, 2, 11, 2, 76, 1, 3, 4, 1, 1, 1, 2, 4, 1, 79, 1, 1, 1, 10, 1, 1, 2, 1, 2, 2, 2, 18, 14, 3, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 49, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 3, 4, 3, 3, 103, 23, 1, 2, 4, 17, 4, 2, 8, 77, 5, 1, 49, 1, 6, 1, 2, 4, 3, 19, 4, 4, 6, 7, 1, 1, 2, 1, 2, 99, 1, 1, 5, 1, 6, 1, 2, 3, 4, 1, 2, 6, 5, 1, 2, 6, 2, 1, 1, 2, 1, 62, 5, 1, 1, 2, 2, 1, 27, 1, 2, 2, 10, 2, 23, 1, 1, 1, 21, 2, 1, 7, 3, 9, 3, 5, 47, 1, 3, 1, 11, 2, 1, 1, 78, 1, 2, 1, 19, 2, 10, 2, 2, 1, 1, 1, 118, 1, 13, 2, 13, 8, 1, 1, 10, 3, 5, 1, 13, 1, 2, 1, 1, 1, 2, 20, 48, 2, 1, 5, 4, 4, 2, 6, 1, 5, 1, 4, 2, 3, 3, 1, 3, 96, 3, 10, 1, 43, 1, 3, 3, 2, 1, 2, 116, 1, 5, 2, 1, 1, 2, 1, 4, 1, 9, 2, 10, 9, 1, 3, 3, 1, 1, 2, 3, 2, 12, 1, 4, 7, 1, 1, 1, 1, 2, 2, 6, 1, 3, 2, 1, 5, 2, 2, 6, 2, 13, 1, 1, 1, 2, 6, 2, 5, 2, 1, 3, 1, 3, 1, 1, 2, 1, 20, 2, 7, 1, 2, 2, 3, 2, 1, 16, 58, 3, 1, 2, 2, 6, 1, 2, 1, 2, 1, 9, 2, 3, 1, 4, 1, 13, 2, 1, 1, 4, 2, 1, 3, 6, 2, 2, 1, 1, 1, 1, 23, 1, 6, 3, 6]
leng = 10000 base = 3 rpf = [Dragon(n) for n in range (0,leng)] rpfBase = [Integer(Mod(rpf[n],base)) for n in range (0,leng)] rpfNumber = seqToReal(rpfBase,base) print(rpfNumber) print(rpfNumber.continued_fraction())
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