A273946 Odd prime factors of generalized Fermat numbers of the form 5^(2^m) + 1 with m >= 0.

3, 13, 17, 257, 313, 641, 769, 2593, 11489, 19457, 65537, 163841, 786433, 1503233, 1655809, 7340033, 14155777, 18395137, 23606273, 29423041, 39714817, 75068993, 167772161, 2483027969, 4643094529, 6616514561, 47148957697, 241931001601, 2748779069441

Offset: 1

Author

Arkadiusz Wesolowski, Jun 05 2016

Keywords

• nonn

Comments

Odd primes p such that the multiplicative order of 5 (mod p) is a power of 2.

References

• Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..37
• 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)
• Harvey Dubner and Wilfrid Keller, Factors of Generalized Fermat Numbers, Math. Comp. 64 (1995), no. 209, pp. 397-405.
• OEIS Wiki, Generalized Fermat numbers

Crossrefs

Cf. A023394, A072982, A199591, A268658, A268662, A273945 (base 3), A273947 (base 6), A273948 (base 7), A273949 (base 11), A273950 (base 12).

Programs

Mathematica

Select[Prime@Range[2, 10^5], IntegerQ@Log[2, MultiplicativeOrder[5, #]] &]