A293623 Fermat pseudoprimes to base 2 that are pentagonal.

7957, 241001, 1419607, 1830985, 1993537, 2134277, 2163001, 2491637, 2977217, 4864501, 5351537, 6952037, 10084177, 11367137, 11433301, 14609401, 21306157, 22591301, 26470501, 26977001, 29581501, 35851037, 44731051, 46517857, 53154337, 55318957, 55610837

Offset

1,1

Comments

Rotkiewicz proved that this sequence is infinite.

Intersection of A001567 and A000326.

The corresponding indices of the pentagonal numbers are 73, 401, 973, 1105, 1153, 1193, 1201, 1289, 1409, 1801, 1889, 2153, 2593, 2753, 2761, ...

References

Andrzej Rotkiewicz, Sur les nombres pseudopremiers pentagonaux, Bull. Soc. Roy. Sci. Liège, Vol. 33 (1964), pp. 261-263.

Links

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

Example

7957 = (3*73^2 - 73)/2 is in the sequence since it is pentagonal, composite, and 2^7956 == 1 (mod 7957).

Mathematica

p[n_]:=(3n^2-n)/2; Select[p[Range[3, 10^4]], PowerMod[2, (# - 1), #]==1 &]

Crossrefs

Cf. A000326, A001567.

Sequence in context: A260959 A316906 A316907 * A316908 A254138 A157660

Adjacent sequences: A293620 A293621 A293622 * A293624 A293625 A293626

Keyword

nonn

Author

Amiram Eldar, Oct 13 2017

Status

approved