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A321870 Fermat pseudoprimes to base 2 that are decagonal.

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%I A321870 #11 Jul 25 2019 06:46:13
%S A321870 1105,1387,2047,3277,6601,13747,16705,19951,31417,74665,83665,88357,
%T A321870 90751,275887,390937,514447,604117,642001,741751,748657,769567,916327,
%U A321870 1092547,1293337,1302451,1433407,1520905,1530787,1809697,1907851,2008597,2205967,2387797
%N A321870 Fermat pseudoprimes to base 2 that are decagonal.
%C A321870 Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.
%C A321870 Intersection of A001567 and A001107.
%C A321870 The corresponding indices of the decagonal numbers are 17, 19, 23, 29, 41, 59, 65, 71, 89, 137, 145, 149, 151, 263, 313, 359, 389, 401, 431, 433, 439, 479, 523, 569, 571, 599, 617, 619, 673, 691, 709, 743, 773, 829, 863, 883, 911, 919, 941, ...
%H A321870 Amiram Eldar, <a href="/A321870/b321870.txt">Table of n, a(n) for n = 1..10000</a>
%H A321870 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 A321870 Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.
%t A321870 dec[n_] := n(4n-3); Select[dec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
%o A321870 (PARI) isok(n) = (n>1) && ispolygonal(n, 10) && !isprime(n) && (Mod(2, n)^n==2); \\ _Daniel Suteu_, Nov 29 2018
%Y A321870 Cf. A001107, A001567, A293623, A293624, A321871.
%K A321870 nonn
%O A321870 1,1
%A A321870 _Amiram Eldar_, Nov 20 2018