A098917 Least k such that k * M(n) * M(n+1) + 1 is prime where M(n) = A000668(n).

2, 6, 4, 16, 36, 6, 42, 24, 172, 18, 52, 54, 6, 130, 2488, 1344, 12420, 5596, 364, 178, 3382, 10516, 44328, 30342, 25770, 47146

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Example

2*(2^2-1)*(2^3-1) + 1 = 43 is prime, so a(1) = 2.
2*(2^3-1)*(2^5-1) + 1 = 435 is composite, 4*(2^3-1)*(2^5-1) + 1 = 867 is composite, 6*(2^3-1)*(2^5-1) + 1 = 1303 is prime, so a(2) = 6.

Mathematica

f[n_] := Module[{k = 1}, While[! PrimeQ[k*n + 1], k++]; k]; f /@ Times @@@ Partition[2^MersennePrimeExponent[Range[15]] - 1, 2, 1] (* Amiram Eldar, Jul 24 2021 *)
Table[k=1; x=(2^MersennePrimeExponent[n]-1)*(2^MersennePrimeExponent[n+1]-1); Monitor[Parallelize[While[True, If[PrimeQ[k*x+1], Break[]]; k++]; k], k], {n, 1, 24}] (* J.W.L. (Jan) Eerland, Jan 01 2024 *)

Crossrefs

Cf. A000668 (Mersenne primes).

Sequence in context: A226718 A181159 A127320 * A366688 A054786 A269372

Adjacent sequences: A098914 A098915 A098916 * A098918 A098919 A098920

Keyword

nonn,more

Author

Pierre CAMI, Oct 17 2004

Extensions

a(15)-a(23) from Amiram Eldar, Jul 24 2021

a(24)-a(25) from J.W.L. (Jan) Eerland, Jan 02 2024

a(26) from Daniel Suteu, Jan 03 2024

Status

approved