A322160 - OEIS

%I #10 Jul 24 2019 10:31:05

%S 8481,14491,29341,62745,196093,396271,526593,2184571,2513841,5256091,

%T 7017193,8137585,13448593,15247621,16053193,16879501,18740971,

%U 20494401,29878381,33704101,35703361,36724591,41607721,42709591,69741001,70593931,80927821,82976181

%N Fermat pseudoprimes to base 2 that are octadecagonal.

%C Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.

%C Intersection of A001567 and A051870.

%C 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 Amiram Eldar, <a href="/A322160/b322160.txt">Table of n, a(n) for n = 1..10000</a>

%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 octadec[n_]:=n(8n-7); Select[octadec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]

%o (PARI) isok(n) = (n>1) && ispolygonal(n, 18) && !isprime(n) && (Mod(2, n)^n==2); \\ _Michel Marcus_, Nov 29 2018

%Y Cf. A001567, A051870, A293623, A293624, A322161.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 29 2018