A139429 Smallest prime p such that M(n)^2 - p*M(n) + 1 is prime with M(n) = A000668(n).

3, 19, 3, 3, 73, 7, 271, 1021, 241, 3, 487, 151, 2971, 35839, 5737, 1723, 81943, 115741, 307, 151549, 231823, 443431, 195163, 9973, 114913, 362599

Offset

2,1

Comments

All primes certified using openpfgw_v12 from primeform group.

Links

Table of n, a(n) for n=2..27.

Example

7*7-3*7+1=29 prime 7=M(2)=2^3-1 so k(2)=3;
31*31-19*31+1=373 prime 31=M(3)=2^5-1 so k(3)=19.

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

Crossrefs

Cf. A000668, A139424, A139425, A139426, A139427, A139428, A139430, A139421.

Sequence in context: A300946 A364298 A078096 * A293699 A258200 A258007

Adjacent sequences: A139426 A139427 A139428 * A139430 A139431 A139432

Keyword

hard,more,nonn

Author

Pierre CAMI, Apr 21 2008

Status

approved