A268658 Numbers k such that 3*2^k + 1 is a prime factor of a generalized Fermat number 5^(2^m) + 1 for some m.

2, 8, 18, 66, 189, 209, 408, 2208, 2816, 3168, 3912, 20909, 54792, 59973, 157169, 303093, 709968, 801978, 1832496, 2145353, 2291610, 5082306, 10829346, 16408818

Offset

1,1

References

Wilfrid Keller, private communication, 2008.

Links

Table of n, a(n) for n=1..24.

Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.

Anders Björn and Hans Riesel, Table errata to “Factors of generalized Fermat numbers”, Math. Comp. 74 (2005), no. 252, p. 2099.

Anders Björn and Hans Riesel, Table errata 2 to "Factors of generalized Fermat numbers", Math. Comp. 80 (2011), pp. 1865-1866.

C. K. Caldwell, Top Twenty page, Generalized Fermat Divisors (base=5)

OEIS Wiki, Generalized Fermat numbers

Prog

(PARI) for(k=1, +oo, p=3*2^k+1; if(ispseudoprime(p), t=znorder(Mod(5, p)); bitand(t, t-1)==0&&print1(k, ", "))) \\ Jeppe Stig Nielsen, Oct 30 2020

Crossrefs

Cf. A199591, A268657, A204620, A268659, A268660, A268661, A268662, A268663, A226366, A268664. Subsequence of A002253.

Sequence in context: A058082 A005675 A054358 * A074128 A061226 A134827

Adjacent sequences: A268655 A268656 A268657 * A268659 A268660 A268661

Keyword

nonn,hard

Author

Arkadiusz Wesolowski, Feb 10 2016

Extensions

a(24) from Jeppe Stig Nielsen, Oct 30 2020

Status

approved