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%I #11 Jul 25 2019 06:46:23
%S 341,645,2465,2821,4033,5461,8321,15841,25761,31621,68101,83333,
%T 162401,219781,282133,348161,530881,587861,653333,710533,722261,
%U 997633,1053761,1082401,1193221,1246785,1333333,1357441,1398101,1489665,1584133,1690501,1735841
%N Fermat pseudoprimes to base 2 that are octagonal.
%C Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
%C Intersection of A001567 and A000567.
%C The corresponding indices of the octagonal numbers are 11, 15, 29, 31, 37, 43, 53, 73, 93, 103, 151, 167, 233, 271, 307, 341, 421, 443, 467, 487, 491, 577, 593, 601, 631, 645, 667, 673, 683, 705, 727, 751, 761, 901, 911, 919, 991, ...
%C First differs from A216170 at n = 505.
%H Amiram Eldar, <a href="/A321868/b321868.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 oct[n_]:=n(3n-2); Select[oct[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
%o (PARI) isok(n) = (n>1) && ispolygonal(n, 8) && !isprime(n) && (Mod(2, n)^n==2); \\ _Daniel Suteu_, Nov 29 2018
%Y Cf. A000567, A001567, A216170, A293623, A293624, A321869.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 20 2018
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