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

Author

Amiram Eldar, Oct 13 2017

Keywords

• nonn

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.

Crossrefs

Cf. A000330, A001567, A293625.

Programs

Mathematica

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