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Numbers k such that 2^(2*k - 1) - 1 is prime.
3

%I #61 Oct 22 2024 05:43:10

%S 2,3,4,7,9,10,16,31,45,54,64,261,304,640,1102,1141,1609,2127,2212,

%T 4845,4971,5607,9969,10851,11605,22249,43122,55252,66025,108046,

%U 378420,429717,628894,699135,1488111,1510689,3486297,6733459,10498006,12018292,12982476,15201229,16291329,18578334

%N Numbers k such that 2^(2*k - 1) - 1 is prime.

%H Mario Fernando Garcia Rivera, <a href="/A138576/b138576.txt">Table of n, a(n) for n = 1..47</a> (derived from A000043)

%F a(n) = (A000043(n+1) + 1)/2. - _Charles R Greathouse IV_, Aug 30 2010

%F a(n) = A146768(n) + 1. - _César Aguilera_, May 27 2020

%e 2^(2*2 - 1) - 1 = 7;

%e 2^(2*3 - 1) - 1 = 31;

%e 2^(2*4 - 1) - 1 = 127.

%t (MersennePrimeExponent[Range[2, 48]] + 1)/2 (* _Amiram Eldar_, Oct 22 2024 *)

%o (PARI) is(n)=isprime(2^(2*n-1)-1) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A000043, A146768.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 13 2008

%E More terms from _Charles R Greathouse IV_, Aug 30 2010

%E More terms from _Mario Fernando Garcia Rivera_, Jul 18 2022