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A157894
Number of composite numbers between exponents of successive Mersenne primes.
1
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
1,4
LINKS
FORMULA
a(n) = A000043(n+1) - A016027(n+1) - A000043(n) + A016027(n). - Amiram Eldar, Oct 17 2024
EXAMPLE
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).
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
KEYWORD
nonn
AUTHOR
Jani Melik, Mar 08 2009, Apr 02 2009
EXTENSIONS
a(34)-a(38) from Robert G. Wilson v, Mar 14 2009
a(39)-a(44) from Amiram Eldar, Oct 17 2024
STATUS
approved