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

Author

Arkadiusz Wesolowski, Feb 10 2016

Keywords

• nonn
• hard

References

• Wilfrid Keller, private communication, 2008.

Links

• 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

Crossrefs

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

Programs

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

Extensions

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