A157890 Number of primes between exponents of successive Mersenne primes.

0, 0, 0, 1, 0, 0, 2, 6, 5, 3, 2, 66, 12, 95, 120, 10, 115, 127, 18, 593, 29, 130, 896, 180, 155, 2032, 3759, 2104, 1841, 6960, 41452, 7555, 28715

Offset

1,7

Comments

a(6) = 0 since 17 is adjacent to 19 (exponent of 7th Mersenne prime); a(7) = 2 since 23 and 29 are between 19 and 31 (exponent of 8th Mersenne prime); a(8) = 6 since 37, 41, 43, 47, 53 and 59 are between 31 and 61 (exponent of 9th Mersenne prime)

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = (PrimePi(A000043(n+1))-PrimePi(A000043(n)))-1 = (A000720(A000043(n+1))-A000720(A000043(n)))-1. [From Jonathan Vos Post, Mar 09 2009]

Crossrefs

Cf. A000040, A000043, A046933

Sequence in context: A336074 A021381 A323501 * A329932 A359858 A198821

Adjacent sequences: A157887 A157888 A157889 * A157891 A157892 A157893

Keyword

nonn

Author

Jani Melik, Mar 08 2009, Mar 10 2009

Status

approved