A273947 Prime factors of generalized Fermat numbers of the form 6^(2^m) + 1 with m >= 0.

7, 17, 37, 257, 353, 1297, 1697, 2753, 18433, 65537, 80897, 98801, 145601, 763649, 3360769, 4709377, 13631489, 50307329, 376037377, 2483027969, 3191106049, 4926056449, 51808043009, 152605556737, 916326983681, 1268357529601, 6597069766657, 40711978221569

Offset: 1

Author

Arkadiusz Wesolowski, Jun 05 2016

Keywords

• nonn

Comments

Primes p other than 5 such that the multiplicative order of 6 (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..34
• 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=6)
• 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, Some factors of the numbers G_n=6^(2^n)+1 and H_n=10^(2^n)+1, Math. Comp. 23 (1969), no. 106, pp. 413-415.

Crossrefs

Cf. A023394, A072982, A078303, A268663, A273945 (base 3), A273946 (base 5), A273948 (base 7), A273949 (base 11), A273950 (base 12).

Programs

Mathematica

Select[Prime@Range[4, 10^5], IntegerQ@Log[2, MultiplicativeOrder[6, #]] &]