A099478 - OEIS

%I #14 Apr 15 2021 04:51:08

%S 2,1,3,1,1,4,3,6,1,1,4,2,9,4,9,14,4,1,3,4,36,5,25,4,10,4,18,3,21,9,9,

%T 21,16,65,12,8,51,1,22,2,30,6,10,63,1,30,15,3,10,1,22,57,202,4,3,53,1,

%U 34,12,10,22,29,28,31,7,6,70,29,16,94,37,51,30,56,19,23,70,50,99,16,34,5

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

%C Least k such that k*A020522(n)-1 is prime. - _Michel Marcus_, Apr 13 2021

%H Robert Israel, <a href="/A099478/b099478.txt">Table of n, a(n) for n = 1..2090</a>

%e 1*2^6*(2^6-1) - 1 = 4031 = 29*139

%e 2*2^6*(2^6-1) - 1 = 8063 = 11*733

%e 3*2^6*(2^6-1) - 1 = 12095 = 5*2419

%e 4*2^6*(2^6-1) - 1 = 16127, which is prime, so a(6)=4.

%p f:= proc(n) local c,k;

%p   c:= 2^n*(2^n-1);

%p for k from 1 do if isprime(c*k-1) then return k fi od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Apr 12 2021

%o (PARI) a(n) = my(k=1); while(!isprime(k*2^n*(2^n-1) - 1), k++); k; \\ _Michel Marcus_, Apr 13 2021

%Y Cf. A020522.

%K nonn

%O 1,1

%A _Pierre CAMI_, Nov 18 2004