A260072 Primes p such that (p-1)^2+1 divides 2^(p-1)-1.

17, 257, 8209, 65537, 649801

Offset: 1

Author

Jaroslav Krizek, Jul 22 2015

Keywords

• nonn
• more

Comments

a(6), if it exists, is larger than 1.7*10^12. - Giovanni Resta, Jul 23 2015

N = 1382401 is the smallest composite number such that (n-1)^2+1 divides 2^(n-1)-1, cf. A260407; see also A081762 and A260406. The sequence contains all Fermat primes 2^2^k+1 > 5 (A019434). - M. F. Hasler, Jul 24 2015

Examples

			17 is in this sequence because (17 - 1)^2 + 1 = 257 divides 2^(17 - 1) - 1 = 65535; 65535 / 257 = 255.
		

Crossrefs

Cf. A081762 (primes p such that (p-1)^2 - 1 divides 2^(p-1) - 1).

Programs

Magma

[n: n in [1..2000000] | IsPrime(n) and (2^(n-1)-1) mod ((n-1)^2 + 1) eq 0];

Mathematica

fQ[n_] := PowerMod[2, n-1, (n-1)^2 + 1] == 1; p = 2; lst = {}; While[p < 10^9, If[ fQ@ p, AppendTo[lst, p]]; p = NextPrime@ p] (* Robert G. Wilson v, Jul 24 2015 *)