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A293624
Fermat pseudoprimes to base 2 that are square pyramidal numbers.
8
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
Andrzej Rotkiewicz, On pyramidal numbers of order 4, Elemente der Mathematik, Vol. 28 (1973), pp. 14-16.
MATHEMATICA
p[n_]:=n(n+1)(2n+1)/6; Select[p[Range[3, 10^6]], PowerMod[2, (#-1), #] == 1 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 13 2017
STATUS
approved