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%I #17 Jul 24 2019 10:32:02
%S 31609,60701,458989,513629,679729,729061,745889,1207361,1994689,
%T 2746589,4361389,4974971,5173601,5444489,6749021,9056501,12659989,
%U 13295281,15525241,15757741,16070429,16705021,20770621,21400481,23822329,23966011,27492581,34003061
%N Fermat pseudoprimes to base 2 that are tetradecagonal.
%C Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
%C Intersection of A001567 and A051866.
%C 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 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 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.
%t tetradec[n_] := n(6n-5); Select[tetradec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
%t Select[PolygonalNumber[14,Range[2400]],PowerMod[2,#-1,#]==1&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 11 2018 *)
%o (PARI) isok(n) = ispolygonal(n, 14) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ _Michel Marcus_, Nov 28 2018
%Y Cf. A001567, A051866, A293623, A293624, A322124.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 27 2018