A321870 - OEIS

%I #11 Jul 25 2019 06:46:13

%S 1105,1387,2047,3277,6601,13747,16705,19951,31417,74665,83665,88357,

%T 90751,275887,390937,514447,604117,642001,741751,748657,769567,916327,

%U 1092547,1293337,1302451,1433407,1520905,1530787,1809697,1907851,2008597,2205967,2387797

%N Fermat pseudoprimes to base 2 that are decagonal.

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

%C Intersection of A001567 and A001107.

%C 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 Amiram Eldar, <a href="/A321870/b321870.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 dec[n_] := n(4n-3); Select[dec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]

%o (PARI) isok(n) = (n>1) && ispolygonal(n, 10) && !isprime(n) && (Mod(2, n)^n==2); \\ _Daniel Suteu_, Nov 29 2018

%Y Cf. A001107, A001567, A293623, A293624, A321871.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 20 2018