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A321870

Fermat pseudoprimes to base 2 that are decagonal.

1105, 1387, 2047, 3277, 6601, 13747, 16705, 19951, 31417, 74665, 83665, 88357, 90751, 275887, 390937, 514447, 604117, 642001, 741751, 748657, 769567, 916327, 1092547, 1293337, 1302451, 1433407, 1520905, 1530787, 1809697, 1907851, 2008597, 2205967, 2387797

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OFFSET

1,1

COMMENTS

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

Intersection of A001567 and A001107.

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, ...

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.

Wikipedia, Schinzel's Hypothesis H.

MATHEMATICA

dec[n_] := n(4n-3); Select[dec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]

PROG

(PARI) isok(n) = (n>1) && ispolygonal(n, 10) && !isprime(n) && (Mod(2, n)^n==2); \\ Daniel Suteu, Nov 29 2018

CROSSREFS

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

Sequence in context: A168629 A175521 A214607 * A257759 A025295 A025314

Adjacent sequences: A321867 A321868 A321869 * A321871 A321872 A321873