A342692 a(n) is the smallest prime p which is greater than the exponent of the n-th Mersenne prime.

3, 5, 7, 11, 17, 19, 23, 37, 67, 97, 109, 131, 523, 613, 1283, 2207, 2287, 3221, 4259, 4441, 9697, 9949, 11239, 19949, 21713, 23227, 44501, 86249, 110527, 132059, 216103, 756853, 859447, 1257827, 1398281, 2976229, 3021407, 6972607, 13466923, 20996023

Offset

1,1

Links

Table of n, a(n) for n=1..40.

GIMPS, Known Mersenne primes

Eric Weisstein's World of Mathematics, Mersenne Prime

Wikipedia, Mersenne Prime

Formula

a(n) = A151800(A000043(n)).

Example

Terms begin as follows:
.                                          a(n) =
  n   n-th Mersenne prime   exponent q  nextprime(q)
  -  ---------------------  ----------  ------------
  1  2^2  - 1 =          3       2            3
  2  2^3  - 1 =          7       3            5
  3  2^5  - 1 =         31       5            7
  4  2^7  - 1 =        127       7           11
  5  2^13 - 1 =       8191      13           17
  6  2^17 - 1 =     131071      17           19
  7  2^19 - 1 =     524287      19           23
  8  2^31 - 1 = 2147483647      31           37

Mathematica

Table[NextPrime[MersennePrimeExponent[n]], {n, 1, 47}]

Crossrefs

Cf. A000043 (Mersenne prime exponents), A000668 (Mersenne primes), A151800 (next prime).

Sequence in context: A128926 A139559 A158361 * A048184 A290283 A163420

Adjacent sequences: A342689 A342690 A342691 * A342693 A342694 A342695

Keyword

hard,less,nonn

Author

David R. Kirkby, May 18 2021

Status

approved