A105181 Numbers k such that 2^(2*(k+1)) + 2^k - 1 is prime.

1, 2, 3, 4, 5, 6, 8, 10, 14, 22, 38, 42, 71, 118, 128, 159, 179, 214, 484, 951, 1148, 1162, 1427, 1532, 1692, 1861, 2261, 3760, 4575, 6974, 7295, 8367, 8463, 8600, 14878, 16165, 24327, 24482, 34600, 35067

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Example

2^4 + 2^1 + 1 = 19 is prime so a(1)=1.
2^6 + 2^2 + 1 = 67 is prime so a(2)=2.
2^8 + 2^3 + 1 = 263 is prime so a(3)=3.

Mathematica

a[n_]:=2^(2*(n+1))+2^n-1; lst={}; Do[If[PrimeQ[a[n]], AppendTo[lst, n]], {n, 0, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 03 2009 *)

Prog

(PARI) is(n)=ispseudoprime(2^(2*(n+1))+2^n-1) \\ Charles R Greathouse IV, Jun 13 2017
(Magma) [k: k in [0..200] | IsPrime(2^(2*(k+1))+2^k-1)]; // Jinyuan Wang, Mar 20 2020

Crossrefs

Cf. A105182.

Sequence in context: A179053 A218949 A129976 * A263361 A320020 A229034

Adjacent sequences: A105178 A105179 A105180 * A105182 A105183 A105184

Keyword

nonn,more

Author

Pierre CAMI, Apr 11 2005

Extensions

a(31)-a(36) from Ryan Propper, Jan 31 2008

a(37)-a(40) from Michael S. Branicky, Oct 12 2024

Status

approved