A178653 Numbers k that 4^k + 13^2 is prime.

1, 3, 5, 7, 9, 13, 15, 31, 33, 47, 65, 99, 103, 147, 197, 203, 257, 399, 411, 471, 497, 979, 1189, 2851, 3221, 4689, 5027, 7131, 7545, 9049, 9849

Offset

1,2

Comments

See A178652.

Links

Table of n, a(n) for n=1..31.

Example

4^1 + 13^2 = 173 = prime(40), 1 is first term.
4^3 + 13^2 = 233 = prime(51), 3 is 2nd term.
4^5 + 13^2 = 1193 = prime(196), 5 is 3rd term.
4^147 + 13^2 = 318286...15753 (89 digits), 147 is 14th term.
4^197 + 13^2 = 403...9753 (119 digits), 197 is 15th term.

Mathematica

fQ[n_] := PrimeQ[(2^k)^2 + 169]; k = 1; lst = {}; While[k < 10^4, If[ fQ@k, AppendTo[lst, k]; Print@k]; k += 2]; lst (* Robert G. Wilson v, Jul 31 2010 *)

Prog

(PARI) forstep(k=1, 999, 2, if(ispseudoprime(4^n+169), print1(n", "))) \\ Charles R Greathouse IV, Aug 27 2013

Crossrefs

Cf. A176969, A176978, A177833, A178652.

Sequence in context: A003524 A243910 A211136 * A222314 A228232 A182058

Adjacent sequences: A178650 A178651 A178652 * A178654 A178655 A178656

Keyword

nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Jun 01 2010

Extensions

a(16)-a(31) from Robert G. Wilson v, Jul 31 2010

New name from Charles R Greathouse IV, Aug 27 2013

Status

approved