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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
 1, 3, 1, 7, 8, 19, 13, 4, 16, 3, 42, 24, 434, 84, 160, 579, 475, 529, 2450, 2644, 3928, 558, 13680, 7146, 1408, 3003, 2369, 55000, 83873 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA 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 EXAMPLE M(4)=2^7-1=127 127^2+127-1=16255 composite (2*127)^2+2*127-1=64769 composite (3*127)^2+3*127-1=145541 composite (4*127)^2+4*127-1=258571 composite (5*127)^2+5*127-1=403859 composite (6*127)^2+6*127-1=581405 composite (7*127)^2+7*127-1=791209 prime so k(4)=7 1*(2^2-1)*(1*(2^2-1)+1)-1=11 prime, 2^2-1 first Mersenne prime, a(1)=1. 3*(2^3-1)*(3*(2^3-1)+1)-1=461 prime, 2^3-1 second Mersenne prime, a(2)=3. 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 PROG (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 CROSSREFS Cf. A121371. Cf. A000043 (Mersenne exponents), A000668 (Mersenne primes). Cf. A137906, A137907, A137909. Sequence in context: A340616 A120472 A271059 * A137908 A229837 A019639 Adjacent sequences:  A121367 A121368 A121369 * A121371 A121372 A121373 KEYWORD hard,more,nonn AUTHOR Pierre CAMI, Jul 24 2006 EXTENSIONS a(21) corrected by Pierre CAMI, Mar 04 2014 a(27)-a(29) by Pierre CAMI, Oct 11 2014 Checked for n = 1..15 by Wolfdieter Lang, Oct 26 2014 Merged with A137908 by Vaclav Kotesovec, Oct 30 2014 STATUS approved

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)