Shared2018-07-10-092720.sagewsOpen in CoCalc
Powers of two with 2/3 multiplier and 1101 chord
# Chord 1101
powersoftwo = [2**n for n in range(16)]
multiplier = .66666666666666666
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+1]*X[i+3]-1 for i in range(len(X)-3)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 2, 5, 10, 21, 42, 85, 170, 341, 682, 1365, 2730, 5461, 10922, 21845] [-1, 19, 209, 2099, 17849, 149939, 1217369, 9854899, 79129049, 634894259, 5083808729, 40700286899, 325676837849] [False, True, False, True, False, True, False, True, True, True, True, True, False]
# Chord 1101
multiplier = .840270996094
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+1]*X[i+3]-1 for i in range(len(X)-3)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 3, 6, 13, 26, 53, 107, 215, 430, 860, 1720, 3441, 6883, 13767, 27534] [-1, 38, 467, 4133, 36165, 296269, 2438529, 19784299, 159013999, 1272481799, 10181333599, 81480264839, 652126352201] [False, False, True, True, False, True, False, False, True, True, True, True, True]
# Chord 1101
multiplier = .737
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+1]*X[i+3]-1 for i in range(len(X)-3)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 2, 5, 11, 23, 47, 94, 188, 377, 754, 1509, 3018, 6037, 12075, 24150] [-1, 21, 229, 2584, 23781, 203227, 1665585, 13324687, 106951883, 857890643, 6868814081, 54991506149, 440004933899] [False, False, True, False, False, True, False, True, True, True, True, True, False]
# Chord 1011
multiplier = .7739868
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+2]*X[i+3]-1 for i in range(len(X)-3)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 3, 6, 12, 24, 49, 99, 198, 396, 792, 1585, 3170, 6340, 12680, 25361] [-1, 71, 863, 7055, 58211, 470447, 3841991, 31049567, 248553359, 1989682199, 15917457599, 127420051999, 1019400611599] [False, True, True, False, True, True, True, True, True, False, False, False, True]
# Chord 111
multiplier = .64093175781
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+1]*X[i+2]-1 for i in range(len(X)-2)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 2, 5, 10, 20, 41, 82, 164, 328, 656, 1312, 2625, 5250, 10501, 21002] [-1, 9, 99, 999, 8199, 67239, 551367, 4410943, 35287551, 282300415, 2259263999, 18080999999, 144716906249, 1157845510499] [False, False, False, False, False, False, False, False, False, False, True, True, True, True]
# Chord 111
multiplier = .775390625
X = [int(multiplier*x) for x in powersoftwo]
prime_chord = [X[i]*X[i+1]*X[i+2]-1 for i in range(len(X)-2)]
print(X)
print(prime_chord)
print([is_prime(p) for p in prime_chord])

[0, 1, 3, 6, 12, 24, 49, 99, 198, 397, 794, 1588, 3176, 6352, 12704, 25408] [-1, 17, 215, 1727, 14111, 116423, 960497, 7781993, 62413163, 500566183, 4004529471, 32036235775, 256289886207, 2050319089663] [False, True, False, False, False, True, True, True, True, False, False, False, False, False]