A176946 -id:A176946 - cp's OEIS frontend

A294134 Sorted list of prime factors of numbers of the form 7^(2^m) + 2^(2^m) with m >= 0.

3, 17, 53, 97, 257, 449, 2417, 7681, 8513, 65537, 89633, 114689, 339121, 876097, 1321729, 1454081, 2572289, 4638721, 5463041, 7340033, 27688961, 47047681, 62177153, 93847553, 113418241, 374734849, 3731619841, 13037142017, 13555990529, 13951408129, 142807662593

Offset: 1

Arkadiusz Wesolowski, Oct 23 2017

nonn

Primes p other than 5 such that the multiplicative order of 7/2 (mod p) is a power of 2.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..43
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.

Cf. A176946, A294132, A294133, A294135, A294136.

print1(3, ", "); forprime(p=17, 142807662593, z=znorder(Mod(7/2, p)); if(2^ispower(z)==z, print1(p, ", ")));

A386618 Primes of the form 2^k + 13^k.

Original entry on oeis.org

2, 173, 815730977

Offset: 1

Vincenzo Librandi, Aug 17 2025

If 13^k + 2^k is prime then k is either 0 or a power of 2. The corresponding values of k for a(1)-a(4) are 0, 2, 8 and 512. The fourth value is too long to enter.

Vincenzo Librandi, Table of n, a(n) for n = 1..4

Cf. A082101, A094475, A094476, A094477, A176946, A176947.

[a: n in [0..200] | IsPrime(a) where a is 13^n+2^n ];

Select[Table[2^n+13^n,{n,0,600}],PrimeQ]

cp's OEIS Frontend

A294134 Sorted list of prime factors of numbers of the form 7^(2^m) + 2^(2^m) with m >= 0.

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