A073715 Prime preceding the n-th Mersenne prime.

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

Offset: 1

Author

Labos Elemer, Aug 05 2002

Keywords

• nonn
• hard

Links

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

Crossrefs

Cf. A000668, A074626, A151799, A365161.

Programs

Maple

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

Mathematica

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 *)

Formula

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)