A217835 Fermat pseudoprimes to base 2 that can be written as p^2*n - p*n + p, where p is also a Fermat pseudoprime to base 2 and n is a positive integer.

348161, 831405, 1246785, 1275681, 2077545, 2513841, 5977153, 9613297, 13333441, 13823601, 18137505, 19523505, 21474181, 21880801, 37695505, 38171953, 44521301, 47734141, 54448153, 72887585, 75151441, 95423329

Offset: 1

Author

Marius Coman, Oct 12 2012

Keywords

• nonn

Comments

After a(22) = 95423329, no more terms through 10^8.

The corresponding (p,n): (341,3), (645,2), (645,3), (341,11), (645,5), (561,8), (1729,2), (1387,5), (341,120), (561,44), (1905,5), (645,47), (3277,2), (2701,3), (2047,9), (4369,2), (341,384), (2821,6), (2047,13), (2465,12), (3277,7), (4369,5).

Conjecture: For any Fermat pseudoprime p to base 2 there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n - p*n + p, where n is a positive integer.

See the sequence A215343: the generalized formula from there is p^2*n - p*n + p^2, which suggests an extrapolated formula for obtaining some Fermat pseudoprime to base 2 from another: p^2*n - p*n + p^k.

Conjecture: For any Fermat pseudoprime p to base 2 and any positive integer k, there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n - p*n + p^k, where n is a positive integer.

Links

• Eric Weisstein's World of Mathematics, Poulet Number

Crossrefs

Cf. A001567, A213812, A215343.