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semiprimemods.py
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semiprimemods.py
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#! /usr/bin/env python3
from labmath import semiprimegen # Available via pip (https://pypi.org/project/labmath/)
from time import time
A106125, A357741 = [], [] # Numbers n such that the nth semiprime == 0 (mod n), and the corresponding semiprimes
A106126, A357781 = [], [] # Numbers n such that the nth semiprime == 1 (mod n), and the corresponding semiprimes
A106127, A356755 = [], [] # Numbers n such that the nth semiprime == 2 (mod n), and the corresponding semiprimes
A106128, A357807 = [], [] # Numbers n such that the nth semiprime == 3 (mod n), and the corresponding semiprimes
A106129, A357808 = [], [] # Numbers n such that the nth semiprime == 4 (mod n), and the corresponding semiprimes
A106130, A357023 = [], [] # Numbers n such that the nth semiprime == 5 (mod n), and the corresponding semiprimes
A106131, A356135 = [], [] # Numbers n such that the nth semiprime == 6 (mod n), and the corresponding semiprimes
A106132, A356357 = [], [] # Numbers n such that the nth semiprime == 7 (mod n), and the corresponding semiprimes
A106133, A106133sp = [], [] # Numbers n such that the nth semiprime == 8 (mod n), and the corresponding semiprimes
A106134, A106134sp = [], [] # Numbers n such that the nth semiprime == 9 (mod n), and the corresponding semiprimes
A106135, A106135sp = [], [] # Numbers n such that the nth semiprime == 10 (mod n), and the corresponding semiprimes
A106136, A106136sp = [], [] # Numbers n such that the nth semiprime == 11 (mod n), and the corresponding semiprimes
A356764 = [] # A357741 / A106125
try:
print("Press ctrl+c at any time to halt computation and print the results thus far.")
z = time()
for (n,s) in enumerate(semiprimegen(), start=1):
if n % 10**6 == 0: print('\b'*80 + "n: %de6 nth semprime: %d seconds: %d" % (n//10**6, s, int(time() - z)), end='', flush=True)
if (s - 0) % n == 0: A106125.append(n); A357741.append(s); A356764.append(s//n)
if (s - 1) % n == 0: A106126.append(n); A357781.append(s)
if (s - 2) % n == 0: A106127.append(n); A356755.append(s)
if (s - 3) % n == 0: A106128.append(n); A357807.append(s)
if (s - 4) % n == 0: A106129.append(n); A357808.append(s)
if (s - 5) % n == 0: A106130.append(n); A357023.append(s)
if (s - 6) % n == 0: A106131.append(n); A356135.append(s)
if (s - 7) % n == 0: A106132.append(n); A356357.append(s)
if (s - 8) % n == 0: A106133.append(n); A106133sp.append(s)
if (s - 9) % n == 0: A106134.append(n); A106134sp.append(s)
if (s - 10) % n == 0: A106135.append(n); A106135sp.append(s)
if (s - 11) % n == 0: A106136.append(n); A106136sp.append(s)
except KeyboardInterrupt:
print()
print("\nA106125:", A106125)
print("\nA106126:", A106126)
print("\nA106127:", A106127)
print("\nA106128:", A106128)
print("\nA106129:", A106129)
print("\nA106130:", A106130)
print("\nA106131:", A106131)
print("\nA106132:", A106132)
print("\nA106133:", A106133)
print("\nA106134:", A106134)
print("\nA106135:", A106135)
print("\nA106136:", A106136)
print()
print("\nA357741:", A106125sp)
print("\nA357781:", A106126sp)
print("\nA356755:", A106127sp)
print("\nA357807:", A106128sp)
print("\nA357808:", A106129sp)
print("\nA357023:", A106130sp)
print("\nA356135:", A106131sp)
print("\nA356357:", A106132sp)
print("\nA106133sp:", A106133sp)
print("\nA106134sp:", A106134sp)
print("\nA106135sp:", A106135sp)
print("\nA106136sp:", A106136sp)
print()
print("\nA356764:", A106125r)
print()
print(n)
"""
A106125: [1, 2, 3, 7, 11, 43, 53, 613367, 613439, 613451, 613523, 613549, 613609, 6384425461, 6384425521, 6384425569, 6384425647]
A106126: [1, 27, 28, 35, 40, 44, 47, 55, 56, 72, 613400, 613401, 613457, 613482, 613530, 613538, 613544, 613550, 613554, 613556, 613560, 613614, 58155520, 58155521, 58155533, 58155537, 58155540, 58155543, 58155545, 58155571, 6384425460, 6384425506, 6384425524, 819217006186, 819217006204, 819217006209, 819217006230, 819217006575, 819217006765, 819217006767, 819217006877, 819217006881, 819217006896, 819217007051]
A106127: [1, 2, 4, 39, 51, 52, 71, 6920, 613377, 613381, 613405, 613433, 613437, 613449, 613455, 613536, 613537, 613548, 613557, 613569, 613581, 613583, 613587, 613588, 613608, 613613, 58155550, 58155570, 6384425447, 6384425465, 6384425505, 6384425531, 6384425567]
A106128: [1, 3, 6, 36, 46, 78, 6915, 6916, 613375, 613378, 613404, 613406, 613414, 613438, 613448, 613454, 613456, 613508, 613519, 613522, 613532, 613559, 613568, 613570, 613582, 613586, 613598, 58155528, 58155536, 58155549, 6384425454, 6384425520, 6384425522, 6384425528, 6384425638, 819217006168, 819217006207, 819217006208, 819217006228, 819217006231, 819217006582, 819217006666, 819217006874, 819217006880, 819217006882, 819217006886, 819217008932]
A106129: [1, 2, 5, 37, 38, 58, 61, 70, 77, 613379, 613413, 613415, 613429, 613485, 613509, 613518, 613521, 613533, 613543, 613599, 6384425449, 6384425459, 6384425463, 6384425517, 6384425557, 6384425574, 6384425634]
A106130: [1, 60, 67, 68, 6919, 613380, 613426, 613558, 613596, 58155532, 58155539, 58155541, 58155542, 58155544, 6384425448, 6384425451, 6384425502, 6384425508, 6384425516, 6384425552, 6384425568, 6384425636, 6384425646, 819217006161, 819217006176, 819217006182, 819217006198, 819217006581, 819217006764, 819217006842, 819217007050]
A106131: [1, 2, 3, 4, 8, 10, 57, 59, 69, 6914, 613376, 613403, 613431, 613432, 613436, 613447, 613453, 613483, 613484, 613507, 613511, 613513, 613516, 613531, 613535, 613541, 613547, 613579, 613580, 613597, 613607, 6384425453, 6384425504, 6384425519, 6384425555, 819217006195, 819217006579, 819217006580, 819217006664, 819217006766, 819217006870]
A106132: [1, 7, 9, 66, 6675, 6918, 613374, 613412, 613418, 613422, 613428, 613434, 613510, 613512, 613514, 613520, 613542, 58155531, 58155569, 58155572, 6384425518, 6384425556, 819217006165, 819217006175, 819217006199, 819217006203, 819217006227, 819217006665, 819217006869]
A106133: [1, 2, 62, 65, 82, 613417, 613423, 613425, 613427, 613435, 613446, 613515, 613517, 613606, 6384425573, 6384425633, 6384425637, 6384425639, 6384425645, 6384425651]
A106134: [1, 3, 5, 6, 13, 15, 80, 86, 6905, 6907, 6908, 6913, 6917, 613373, 613409, 613420, 613421, 613430, 613506, 613534, 613573, 613578, 613600, 58155529, 58155553, 6384425450, 6384425452, 6384425462, 6384425495, 6384425507, 6384425515, 6384425554, 6384425578, 6384425648, 819217006174, 819217006663, 819217006672, 819217006868, 819217006873, 819217006885, 819217008929, 819217008931]
A106135: [1, 2, 4, 12, 14, 64, 79, 81, 83, 84, 85, 6879, 6901, 613419, 613445, 613571, 613605, 58155568, 6384425499, 6384425501, 6384425551, 6384425553, 6384425635, 819217006167, 819217006202, 819217006763, 819217006854, 819217006872]
A106136: [1, 11, 98, 106, 108, 110, 6877, 6878, 6881, 6902, 6903, 6904, 6906, 6912, 613408, 613410, 613411, 613416, 613424, 613572, 613602, 58155530, 58155551, 58155552, 58155566, 58155567, 58155573, 6384425514, 6384425640, 819217006169, 819217006170, 819217006181, 819217006197, 819217006200, 819217006855, 819217006884, 819217007049, 819217008934]
A357741: [4, 6, 9, 21, 33, 129, 159, 3066835, 3067195, 3067255, 3067615, 3067745, 3068045, 44690978227, 44690978647, 44690978983, 44690979529]
A357781: [4, 82, 85, 106, 121, 133, 142, 166, 169, 217, 3067001, 3067006, 3067286, 3067411, 3067651, 3067691, 3067721, 3067751, 3067771, 3067781, 3067801, 3068071, 348933121, 348933127, 348933199, 348933223, 348933241, 348933259, 348933271, 348933427, 44690978221, 44690978543, 44690978669, 6553736049489, 6553736049633, 6553736049673, 6553736049841, 6553736052601, 6553736054121, 6553736054137, 6553736055017, 6553736055049, 6553736055169, 6553736056409]
A356755: [4, 6, 10, 119, 155, 158, 215, 27682, 3066887, 3066907, 3067027, 3067167, 3067187, 3067247, 3067277, 3067682, 3067687, 3067742, 3067787, 3067847, 3067907, 3067917, 3067937, 3067942, 3068042, 3068067, 348933302, 348933422, 44690978131, 44690978257, 44690978537, 44690978719, 44690978971]
A357807: [4, 9, 15, 111, 141, 237, 27663, 27667, 3066878, 3066893, 3067023, 3067033, 3067073, 3067193, 3067243, 3067273, 3067283, 3067543, 3067598, 3067613, 3067663, 3067798, 3067843, 3067853, 3067913, 3067933, 3067993, 348933171, 348933219, 348933297, 44690978181, 44690978643, 44690978657, 44690978699, 44690979469, 6553736049347, 6553736049659, 6553736049667, 6553736049827, 6553736049851, 6553736052659, 6553736053331, 6553736054995, 6553736055043, 6553736055059, 6553736055091, 6553736071459]
A357808: [4, 6, 14, 115, 118, 178, 187, 214, 235, 3066899, 3067069, 3067079, 3067149, 3067429, 3067549, 3067594, 3067609, 3067669, 3067719, 3067999, 44690978147, 44690978217, 44690978245, 44690978623, 44690978903, 44690979022, 44690979442]
A357023: [4, 185, 206, 209, 27681, 3066905, 3067135, 3067795, 3067985, 348933197, 348933239, 348933251, 348933257, 348933269, 44690978141, 44690978162, 44690978519, 44690978561, 44690978617, 44690978869, 44690978981, 44690979457, 44690979527, 6553736049293, 6553736049413, 6553736049461, 6553736049589, 6553736052653, 6553736054117, 6553736054741, 6553736056405]
A356135: [4, 6, 9, 10, 22, 26, 177, 183, 213, 27662, 3066886, 3067021, 3067161, 3067166, 3067186, 3067241, 3067271, 3067421, 3067426, 3067541, 3067561, 3067571, 3067586, 3067661, 3067681, 3067711, 3067741, 3067901, 3067906, 3067991, 3068041, 44690978177, 44690978534, 44690978639, 44690978891, 6553736049566, 6553736052638, 6553736052646, 6553736053318, 6553736054134, 6553736054966]
A356357: [4, 21, 25, 205, 26707, 27679, 3066877, 3067067, 3067097, 3067117, 3067147, 3067177, 3067557, 3067567, 3067577, 3067607, 3067717, 348933193, 348933421, 348933439, 44690978633, 44690978899, 6553736049327, 6553736049407, 6553736049599, 6553736049631, 6553736049823, 6553736053327, 6553736054959]
A106133sp: [4, 6, 194, 203, 254, 3067093, 3067123, 3067133, 3067143, 3067183, 3067238, 3067583, 3067593, 3068038, 44690979019, 44690979439, 44690979467, 44690979481, 44690979523, 44690979565]
A106134sp: [4, 9, 14, 15, 35, 39, 249, 267, 27629, 27637, 27641, 27661, 27677, 3066874, 3067054, 3067109, 3067114, 3067159, 3067539, 3067679, 3067874, 3067899, 3068009, 348933183, 348933327, 44690978159, 44690978173, 44690978243, 44690978474, 44690978558, 44690978614, 44690978887, 44690979055, 44690979545, 6553736049401, 6553736053313, 6553736053385, 6553736054953, 6553736054993, 6553736055089, 6553736071441, 6553736071457]
A106135sp: [4, 6, 10, 34, 38, 202, 247, 253, 259, 262, 265, 27526, 27614, 3067105, 3067235, 3067865, 3068035, 348933418, 44690978503, 44690978517, 44690978867, 44690978881, 44690979455, 6553736049346, 6553736049626, 6553736054114, 6553736054842, 6553736054986]
A106136sp: [4, 33, 305, 329, 335, 341, 27519, 27523, 27535, 27619, 27623, 27627, 27635, 27659, 3067051, 3067061, 3067066, 3067091, 3067131, 3067871, 3068021, 348933191, 348933317, 348933323, 348933407, 348933413, 348933449, 44690978609, 44690979491, 6553736049363, 6553736049371, 6553736049459, 6553736049587, 6553736049611, 6553736054851, 6553736055083, 6553736056403, 6553736071483]
A356764: [4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7]
The index sequences have no further terms <= 10^12.
The semiprime sequences have no further terms <= 8040423200947.
The semiprime sequences for remainders 8, 9, 10, and 11 have been rejected by the OEIS.
"""