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A322123 Fermat pseudoprimes to base 2 that are tetradecagonal.

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%I A322123 #17 Jul 24 2019 10:32:02
%S A322123 31609,60701,458989,513629,679729,729061,745889,1207361,1994689,
%T A322123 2746589,4361389,4974971,5173601,5444489,6749021,9056501,12659989,
%U A322123 13295281,15525241,15757741,16070429,16705021,20770621,21400481,23822329,23966011,27492581,34003061
%N A322123 Fermat pseudoprimes to base 2 that are tetradecagonal.
%C A322123 Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
%C A322123 Intersection of A001567 and A051866.
%C A322123 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, ...
%H A322123 Amiram Eldar, <a href="/A322123/b322123.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A322123 Andrzej Rotkiewicz, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa21/aa21137.pdf">On some problems of W. Sierpinski</a>, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.
%H A322123 Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.
%t A322123 tetradec[n_] := n(6n-5); Select[tetradec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
%t A322123 Select[PolygonalNumber[14,Range[2400]],PowerMod[2,#-1,#]==1&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 11 2018 *)
%o A322123 (PARI) isok(n) = ispolygonal(n, 14) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ _Michel Marcus_, Nov 28 2018
%Y A322123 Cf. A001567, A051866, A293623, A293624, A322124.
%K A322123 nonn
%O A322123 1,1
%A A322123 _Amiram Eldar_, Nov 27 2018