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 A121370 Least number k such that (k*M(n))^2 + k*M(n) - 1 is prime with M(i)=i-th Mersenne prime. 3

%I

%S 1,3,1,7,8,19,13,4,16,3,42,24,434,84,160,579,475,529,2450,2644,3928,

%T 558,13680,7146,1408,3003,2369,55000,83873

%N Least number k such that (k*M(n))^2 + k*M(n) - 1 is prime with M(i)=i-th Mersenne prime.

%F a(n) is the least k >= 1 for which k*Mp(n)*(k*Mp(n) + 1) - 1 is prime, where Mp(n) = A000668(n) (see Name). - _Wolfdieter Lang_, Oct 26 2014

%e M(4)=2^7-1=127

%e 127^2+127-1=16255 composite

%e (2*127)^2+2*127-1=64769 composite

%e (3*127)^2+3*127-1=145541 composite

%e (4*127)^2+4*127-1=258571 composite

%e (5*127)^2+5*127-1=403859 composite

%e (6*127)^2+6*127-1=581405 composite

%e (7*127)^2+7*127-1=791209 prime so k(4)=7

%e 1*(2^2-1)*(1*(2^2-1)+1)-1=11 prime, 2^2-1 first Mersenne prime, a(1)=1.

%e 3*(2^3-1)*(3*(2^3-1)+1)-1=461 prime, 2^3-1 second Mersenne prime, a(2)=3.

%e n=6: Mp(6) = 131071 and 19*131071*(19*131071 + 1) - 1 = 6201840632149 which is prime, and for k=1..18 no prime appears. - _Wolfdieter Lang_, Oct 26 2014

%o (PARI) lista() = {v = readvec("b000043.txt"); for (i=1, #v, mp = 2^v[i] - 1; k=1; while (!isprime(k*mp*(k*mp + 1) - 1), k++); print1(k, ", "););} \\ _Michel Marcus_, Oct 27 2014

%Y Cf. A121371.

%Y Cf. A000043 (Mersenne exponents), A000668 (Mersenne primes).

%Y Cf. A137906, A137907, A137909.

%K hard,more,nonn

%O 1,2

%A _Pierre CAMI_, Jul 24 2006

%E a(21) corrected by _Pierre CAMI_, Mar 04 2014

%E a(27)-a(29) by _Pierre CAMI_, Oct 11 2014

%E Checked for n = 1..15 by _Wolfdieter Lang_, Oct 26 2014

%E Merged with A137908 by _Vaclav Kotesovec_, Oct 30 2014

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Last modified August 1 17:21 EDT 2021. Contains 346402 sequences. (Running on oeis4.)