A293624 Fermat pseudoprimes to base 2 that are square pyramidal numbers.

24301222105, 34200607741, 194305088689, 7362505969365, 19702357790989, 2985533798982149, 6091629437910701, 24781034010920641, 98129837465651129, 99860491537987361, 105697961209955269, 154533752639483489, 406611602100644641, 714567498159333701

Offset

1,1

Comments

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

Intersection of A001567 and A000330.

The corresponding indices of A000330 are 4177, 4681, 8353, 28057, 38953, 207673, 263401, 420481, 665233, 669121, 681913, 773953, ...

Links

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

Andrzej Rotkiewicz, On pyramidal numbers of order 4, Elemente der Mathematik, Vol. 28 (1973), pp. 14-16.

Wikipedia, Schinzel's Hypothesis H.

Mathematica

p[n_]:=n(n+1)(2n+1)/6; Select[p[Range[3, 10^6]], PowerMod[2, (#-1), #] == 1 &]

Crossrefs

Cf. A000330, A001567, A293625.

Sequence in context: A015399 A129475 A172612 * A238356 A234064 A017290

Adjacent sequences: A293621 A293622 A293623 * A293625 A293626 A293627

Keyword

nonn

Author

Amiram Eldar, Oct 13 2017

Status

approved