A139424 - OEIS

A139424

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

1, 1, 1, 1, 1, 43, 1, 41, 53, 91, 317, 317, 43, 1, 37, 3595, 563, 17239, 911, 11497, 58501, 1259, 10283, 138569, 72247, 27733, 11777, 179105

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OFFSET

1,6

COMMENTS

All primes certified using openpfgw_v12 from primeform group

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

3*3-1*3-1=5 prime 3=M(1)=2^2-1 so k(1)=1;

7*7-1*7-1=41 prime 7=M(2)=2^3-1 so k(2)=1;

31*31-1*31-1=929 prime 31=M(3)=2^5-1 so k(3)=1.

MATHEMATICA

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};

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

While[! PrimeQ[m2 - k*m - 1], k++]; k, {n, 15}] (* Robert Price, Apr 17 2019 *)

CROSSREFS

Cf. A000668, A139425, A139426, A139427, A139428, A139429, A139430, A139421.

Sequence in context: A291871 A357001 A114786 * A051318 A036202 A212316

Adjacent sequences: A139421 A139422 A139423 * A139425 A139426 A139427

KEYWORD

hard,more,nonn

AUTHOR

Pierre CAMI, Apr 21 2008

EXTENSIONS

a(27)-a(28) from Robert Price, May 09 2019

STATUS

approved