This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157894 #18 Oct 17 2024 12:15:53
%S A157894 0,1,1,4,3,1,9,23,22,14,17,327,73,576,803,67,820,908,151,4672,222,
%T A157894 1141,7827,1583,1352,19255,37986,22155,19704,77081,499295,95038,
%U A157894 369638,130508,1469735,42125,3694547,6091617,7076983,2861035,1815190,4178608,2054002,4310827
%N A157894 Number of composite numbers between exponents of successive Mersenne primes.
%H A157894 Amiram Eldar, <a href="/A157894/b157894.txt">Table of n, a(n) for n = 1..47</a>
%F A157894 a(n) = A000043(n+1) - A016027(n+1) - A000043(n) + A016027(n). - _Amiram Eldar_, Oct 17 2024
%e A157894 a(1) = 0 since 2 is adjacent to 3 (exponent of 2nd Mersenne prime).
%e A157894 a(2) = 1 since 4 is between 3 and 5 (exponent of 3rd Mersenne prime).
%e A157894 a(3) = 1 since 6 is between 5 and 7 (exponent of 4th Mersenne prime).
%e A157894 a(4) = 4 since 8, 9, 10, and 12 are between 7 and 13 (exponent of 5th Mersenne prime).
%t A157894 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 *)
%Y A157894 Cf. A000043, A002808, A016027, A046933.
%K A157894 nonn
%O A157894 1,4
%A A157894 _Jani Melik_, Mar 08 2009, Apr 02 2009
%E A157894 a(34)-a(38) from _Robert G. Wilson v_, Mar 14 2009
%E A157894 a(39)-a(44) from _Amiram Eldar_, Oct 17 2024