A365161 -id:A365161 - cp's OEIS frontend

A073715 Prime preceding the n-th Mersenne prime.

2, 5, 29, 113, 8179, 131063, 524269, 2147483629, 2305843009213693921, 618970019642690137449562091, 162259276829213363391578010287957, 170141183460469231731687303715884105703

Offset: 1

Labos Elemer, Aug 05 2002

Amiram Eldar, Table of n, a(n) for n = 1..18

Cf. A000668, A074626, A151799, A365161.

a:= n-> prevprime(numtheory[mersenne]([n])):
seq(a(n), n=1..12);  # Alois P. Heinz, Oct 30 2024

NextPrime[Select[2^Prime[Range[50]] - 1, PrimeQ], -1] (* Jayanta Basu, Jul 08 2013 *)
Table[NextPrime[2^MersennePrimeExponent[n] - 1, -1], {n, 1, 12}] (* Amiram Eldar, Aug 10 2024 *)

a(n) = prime(primepi(A000668(n))-1).
From Amiram Eldar, Aug 10 2024: (Start)
a(n) = A151799(A000668(n)).
a(n) = A000668(n) - A365161(n). (End)

A365160 Least k such that A000668(n) + k is prime, where A000668(n) is the n-th Mersenne prime.

Original entry on oeis.org

2, 4, 6, 4, 18, 30, 22, 12, 16, 30, 40, 30, 888, 486, 2056, 696, 310, 718, 4692, 1600, 2788, 4290, 4326, 4150, 18088, 22096, 16342, 72816, 181720, 4200, 58416

Offset: 1

Robert P. P. McKone, Aug 24 2023

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

			A000668(6) = 131071, the next prime is 131101, so a(6) = 131101 - 131071 = 30.

Cf. A000040, A000668 (Mersenne primes), A001223, A059305, A074626, A365161.

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}]

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

a(n) = A074626(n) - A000668(n). - Amiram Eldar, Aug 10 2024

a(28) from Michael S. Branicky, Aug 11 2024
a(29) from Minfeng Wang, Oct 29 2024
a(30)-a(31) from Minfeng Wang, Oct 29 2024

cp's OEIS Frontend

A073715 Prime preceding the n-th Mersenne prime.

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