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A322160 Fermat pseudoprimes to base 2 that are octadecagonal.

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%I A322160 #10 Jul 24 2019 10:31:05
%S A322160 8481,14491,29341,62745,196093,396271,526593,2184571,2513841,5256091,
%T A322160 7017193,8137585,13448593,15247621,16053193,16879501,18740971,
%U A322160 20494401,29878381,33704101,35703361,36724591,41607721,42709591,69741001,70593931,80927821,82976181
%N A322160 Fermat pseudoprimes to base 2 that are octadecagonal.
%C A322160 Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
%C A322160 Intersection of A001567 and A051870.
%C A322160 The corresponding indices of the octadecagonal numbers are 33, 43, 61, 89, 157, 223, 257, 523, 561, 811, 937, 1009, 1297, 1381, 1417, 1453, 1531, ...
%H A322160 Amiram Eldar, <a href="/A322160/b322160.txt">Table of n, a(n) for n = 1..10000</a>
%H A322160 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 A322160 Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.
%t A322160 octadec[n_]:=n(8n-7); Select[octadec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
%o A322160 (PARI) isok(n) = (n>1) && ispolygonal(n, 18) && !isprime(n) && (Mod(2, n)^n==2); \\ _Michel Marcus_, Nov 29 2018
%Y A322160 Cf. A001567, A051870, A293623, A293624, A322161.
%K A322160 nonn
%O A322160 1,1
%A A322160 _Amiram Eldar_, Nov 29 2018