A273945 Odd prime factors of generalized Fermat numbers of the form 3^(2^m) + 1 with m >= 0.

5, 17, 41, 193, 257, 12289, 59393, 65537, 275201, 786433, 790529, 8972801, 13631489, 21523361, 134382593, 155189249, 448524289, 524455937, 847036417, 3221225473, 12348030977, 22320686081, 77309411329, 206158430209, 4638564679681, 6597069766657, 12079910333441

Offset: 1

Author

Arkadiusz Wesolowski, Jun 05 2016

Keywords

• nonn

Comments

Odd primes p such that the multiplicative order of 3 (mod p) is a power of 2.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..35
• 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=3)
• Harvey Dubner and Wilfrid Keller, Factors of Generalized Fermat Numbers, Math. Comp. 64 (1995), no. 209, pp. 397-405.
• OEIS Wiki, Generalized Fermat numbers
• Hans Riesel, Common prime factors of the numbers A_n=a^(2^n)+1, BIT 9 (1969), pp. 264-269.

Crossrefs

Cf. A023394, A059919, A072982, A268657, A268661, A273946 (base 5), A273947 (base 6), A273948 (base 7), A273949 (base 11), A273950 (base 12).

Programs

Mathematica

Select[Prime@Range[2, 10^5], IntegerQ@Log[2, MultiplicativeOrder[3, #]] &]