A365161 Least k such that A000668(n) - k is prime, where A000668(n) is the n-th Mersenne prime.

1, 2, 2, 14, 12, 8, 18, 18, 30, 20, 170, 24, 114, 56, 156, 2510, 1824, 12, 3980, 3630, 16902, 284, 7712, 20022, 12930, 9698, 16232, 1058, 256016, 23712, 26298

Offset: 1

Author

Robert P. P. McKone, Aug 24 2023

Keywords

• nonn
• hard
• more

Comments

The distance between the n-th Mersenne prime and the previous prime.

Examples

			A000668(6) = 131071, the previous prime is 131063, so a(6) = 131071 - 131063 = 8.
		

Crossrefs

Cf. A000040, A000668 (Mersenne primes), A001223, A059305, A073715, A365160.

Programs

Mathematica

m[n_] := m[n] = (2^MersennePrimeExponent[n] - 1); a[k_, n_] := a[k, n] = m[n] - k; l[k_, n_] := l[k, n] = PrimeQ[a[k, n]]; Table[k = 1; Monitor[Parallelize[While[True, If[l[k, n], Break[]]; k++]; k], {n, k}], {n, 1, 20}]

Formula

a(n) = A001223(A059305(n)-1). - Michel Marcus, Aug 25 2023

a(n) = A000668(n) - A073715(n). - Amiram Eldar, Aug 10 2024

Extensions

a(29)-a(31) from Michael S. Branicky, Sep 01 2024