A294132 Sorted list of prime factors of numbers of the form 3^(2^m) + 2^(2^m) with m >= 0.

5, 13, 17, 97, 257, 401, 769, 1153, 3041, 14177, 65537, 286721, 1810433, 2752513, 4043777, 7340033, 13631489, 23068673, 72222721, 319291393, 348061697, 625483777, 3937533953, 54498164737, 106216554497, 121899667073, 151597350913, 342456532993

Offset

1,1

Comments

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

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..48

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.

Example

The first 5 such numbers are 5, 13, 97, 6817, 43112257, 1853024483819137. Their prime factorizations are (5), (13), (97), (17) (401), (14177) (3041), (1153) (1607133116929). - N. J. A. Sloane, Oct 29 2017

Prog

(PARI) print1(5, ", "); forprime(p=13, 342456532993, z=znorder(Mod(3/2, p)); if(2^ispower(z)==z, print1(p, ", ")));

Crossrefs

Cf. A050244, A094499, A082101, A294133, A294134, A294135, A294136.

Sequence in context: A145040 A361563 A195549 * A125146 A051900 A275800

Adjacent sequences: A294129 A294130 A294131 * A294133 A294134 A294135

Keyword

nonn

Author

Arkadiusz Wesolowski, Oct 23 2017

Status

approved