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 A322123 Fermat pseudoprimes to base 2 that are tetradecagonal. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite. Intersection of A001567 and A051866. 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, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale) Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259. Wikipedia, Schinzel's Hypothesis H. MATHEMATICA 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 *) PROG (PARI) isok(n) = ispolygonal(n, 14) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ Michel Marcus, Nov 28 2018 CROSSREFS Cf. A001567, A051866, A293623, A293624, A322124. Sequence in context: A234205 A236136 A192102 * A236062 A187728 A154471 Adjacent sequences:  A322120 A322121 A322122 * A322124 A322125 A322126 KEYWORD nonn AUTHOR Amiram Eldar, Nov 27 2018 STATUS approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)