A204388 Numbers k such that 4^k + 25 is prime.

1, 2, 3, 4, 5, 10, 11, 17, 35, 46, 56, 59, 118, 125, 189, 219, 285, 327, 400, 818, 1424, 2474, 2835, 3386, 3747, 4003, 4528, 5519, 8134, 10708, 10869, 16685, 39353, 56065, 63223, 82023, 109625, 118216, 184024, 262077, 265405, 320427, 349870, 373151, 377019, 377188, 465988, 494781

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 15 2012

Keywords

• nonn

Comments

a(40) > 2.5*10^5. - Robert Price, Oct 17 2015

Since 4^(6k) + 25 = 4096^k + 25 == (1^k + 25) mod 13 = 26 mod 13 == 0 mod 13, no multiple of 6 will be in this sequence. - Timothy L. Tiffin, Aug 07 2016

Examples

			From _Timothy L. Tiffin_, Aug 09 2016: (Start)
 a(1) = 1, since 4^1 + 25 = 4 + 25 = 29, which is prime.
 a(2) = 2, since 4^2 + 25 = 16 + 25 = 41, which is prime.
 a(3) = 3, since 4^3 + 25 = 64 + 25 = 89, which is prime.
 a(4) = 4, since 4^4 + 25 = 256 + 25 = 281, which is prime.
 a(5) = 5, since 4^5 + 25 = 1024 + 25 = 1049, which is prime.
 a(6) = 10, since 4^10 + 25 = 1048576 + 25 = 1048601, which is prime. (End)
		

Crossrefs

Cf. A057196, A104072, A157006.

Programs

Magma

[n: n in [1..1000] | IsPrime(4^n+25)]; // Vincenzo Librandi, Aug 07 2016

Mathematica

Select[Range[2000], PrimeQ[4^# + 25] &] (* T. D. Noe, Feb 03 2012 *)

PARI

for(n=1, 1e5, if(isprime(4^n + 25), print1(n", "))) \\ Altug Alkan, Oct 17 2015

Formula

a(n) = A157006(n)/2. - Robert Price, Oct 17 2015

Extensions

a(22)-a(39) derived from A157006 by Robert Price, Oct 17 2015

a(40)-a(48) derived from A157006 by Elmo R. Oliveira, Nov 28 2023