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, 7076983, 2861035, 1815190, 4178608, 2054002, 4310827

Offset: 1

Author

Jani Melik, Mar 08 2009, Apr 02 2009

Keywords

• nonn

Examples

			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

• Amiram Eldar, Table of n, a(n) for n = 1..47

Crossrefs

Cf. A000043, A002808, A016027, A046933.

Programs

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 *)

Formula

a(n) = A000043(n+1) - A016027(n+1) - A000043(n) + A016027(n). - Amiram Eldar, Oct 17 2024

Extensions

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

a(39)-a(44) from Amiram Eldar, Oct 17 2024