A139426 - OEIS

%I #11 Jul 24 2023 10:26:32

%S 1,5,1,5,11,11,17,19,23,97,127,145,167,269,767,479,3307,1453,18007,

%T 2357,599,17669,5527,3191,3251,70249,147773,39637

%N Smallest number k such that M(n)^2+k*M(n)-1 is prime with M(n)= Mersenne primes =A000668(n).

%C All primes certified using openpfgw_v12 from primeform group.

%e 3*3+1*3-1=11 prime 3=M(1)=2^2-1 so k(1)=1;

%e 7*7+5*7-1=83 prime 7=M(2)=2^3-1 so k(2)=5;

%e 31*31+1*31-1=991 prime 31=M(3)=2^5-1 so k(3)=1.

%t A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609};

%t Table[m = 2^A000043[[n]] - 1; m2 = m^2; k = 1;

%t While[! PrimeQ[m2 + k*m - 1], k++]; k, {n, 15}] (* _Robert Price_, Apr 17 2019 *)

%Y Cf. A000668, A139424, A139425, A139427, A139428, A139429, A139430, A139421, A143385.

%K hard,more,nonn

%O 1,2

%A _Pierre CAMI_, Apr 21 2008

%E 3 more terms. - _Pierre CAMI_, Aug 11 2008