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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

Formula

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

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

Example

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

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}]

Crossrefs

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

Sequence in context: A068511 A306544 A060590 * A129083 A045685 A045676

Adjacent sequences: A365158 A365159 A365160 * A365162 A365163 A365164

Keyword

nonn,hard,more

Author

Robert P. P. McKone, Aug 24 2023

Extensions

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

Status

approved