A157891 Number of natural numbers between exponents of successive Mersenne primes.

0, 1, 1, 5, 3, 1, 11, 29, 27, 17, 19, 393, 85, 671, 923, 77, 935, 1035, 169, 5265, 251, 1271, 8723, 1763, 1507, 21287, 41745, 24259, 21545, 84041, 540747, 102593, 398353, 140481, 1577951, 45155, 3951215, 6494323

Offset

1,4

Comments

a(0) = 0 since 2 is adjacent to 3 (exponent of 2nd Mersenne prime); a(2) = 1 since 4 is between 3 and 5 (exponent of 3rd Mersenne prime); a(3) = 1 since 6 is between 5 and 7 (exponent of 4th Mersenne prime); a(4) = 5 since 8, 9, 10, 11, and 12 are between 7 and 13 (exponent 5th Mersenne prime).

Links

Table of n, a(n) for n=1..38.

Formula

a(n) = (A000043(n+1)-A000043(n))-1. [From Jonathan Vos Post, Mar 09 2009]

Mathematica

Differences[MersennePrimeExponent[Range[40]]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 09 2020 *)

Crossrefs

Cf. A000027, A000043, A046933

Sequence in context: A021192 A074396 A229958 * A173644 A115991 A352136

Adjacent sequences: A157888 A157889 A157890 * A157892 A157893 A157894

Keyword

nonn

Author

Jani Melik, Mar 08 2009, Mar 09 2009

Status

approved