A157894 Number of composite numbers between exponents of successive Mersenne primes.

0, 1, 1, 4, 3, 1, 9, 23, 22, 14, 17, 327, 73, 576, 803, 67, 820, 908, 151, 4672, 222, 1141, 7827, 1583, 1352, 19255, 37986, 22155, 19704, 77081, 499295, 95038, 369638, 130508, 1469735, 42125, 3694547, 6091617

Offset

1,4

Comments

a(1) = 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) = 4 since 8, 9, 10, and 12 are between 7 and 13 (exponent of 5th Mersenne prime).

Links

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

Mathematica

mp={ (*A000043 *) }; lst = {}; Do[ c = mp[[n + 1]] - mp[[n]] - PrimePi@ mp[[n + 1]] + PrimePi@ mp[[n]]; AppendTo[lst, c], {n, 38}]; lst (* Robert G. Wilson v, Mar 14 2009 *)

Crossrefs

A002808, A000043, A046933

Sequence in context: A123160 A109692 A039758 * A172106 A128813 A109062

Adjacent sequences: A157891 A157892 A157893 * A157895 A157896 A157897

Keyword

nonn

Author

Jani Melik, Mar 08 2009, Apr 02 2009

Extensions

a(34) - a(38) from Robert G. Wilson v, Mar 14 2009

Status

approved