Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Oct 13 2024 06:19:02
%S 1,2,3,4,5,6,8,10,14,22,38,42,71,118,128,159,179,214,484,951,1148,
%T 1162,1427,1532,1692,1861,2261,3760,4575,6974,7295,8367,8463,8600,
%U 14878,16165,24327,24482,34600,35067
%N Numbers k such that 2^(2*(k+1)) + 2^k - 1 is prime.
%e 2^4 + 2^1 + 1 = 19 is prime so a(1)=1.
%e 2^6 + 2^2 + 1 = 67 is prime so a(2)=2.
%e 2^8 + 2^3 + 1 = 263 is prime so a(3)=3.
%t 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 *)
%o (PARI) is(n)=ispseudoprime(2^(2*(n+1))+2^n-1) \\ _Charles R Greathouse IV_, Jun 13 2017
%o (Magma) [k: k in [0..200] | IsPrime(2^(2*(k+1))+2^k-1)]; // _Jinyuan Wang_, Mar 20 2020
%Y Cf. A105182.
%K nonn,more
%O 1,2
%A _Pierre CAMI_, Apr 11 2005
%E a(31)-a(36) from _Ryan Propper_, Jan 31 2008
%E a(37)-a(40) from _Michael S. Branicky_, Oct 12 2024