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A322123
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Fermat pseudoprimes to base 2 that are tetradecagonal.
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4
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31609, 60701, 458989, 513629, 679729, 729061, 745889, 1207361, 1994689, 2746589, 4361389, 4974971, 5173601, 5444489, 6749021, 9056501, 12659989, 13295281, 15525241, 15757741, 16070429, 16705021, 20770621, 21400481, 23822329, 23966011, 27492581, 34003061
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OFFSET
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1,1
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COMMENTS
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Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
The corresponding indices of the tetradecagonal numbers are 73, 101, 277, 293, 337, 349, 353, 449, 577, 677, 853, 911, 929, 953, 1061, 1229, 1453, 1489, 1609, 1621, 1637, 1669, 1861, 1889, 1993, 1999, ...
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LINKS
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MATHEMATICA
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tetradec[n_] := n(6n-5); Select[tetradec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
Select[PolygonalNumber[14, Range[2400]], PowerMod[2, #-1, #]==1&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 11 2018 *)
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PROG
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(PARI) isok(n) = ispolygonal(n, 14) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ Michel Marcus, Nov 28 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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