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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

Table of n, a(n) for n=1..29.

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.)