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 A176559 #17 Jul 31 2025 11:12:16
%S A176559 1,6,19,996,11222,31138,105054174,55890483939986569,
%T A176559 10201730748372641087928204
%N A176559 The number of primes between two consecutive Mersenne primes.
%H A176559 G. L. Honaker, Jr. and C. Caldwell, <a href="https://t5k.org/curios/page.php?curio_id=22859">19</a>, Prime Curios!.
%F A176559 a(n) = A059305(n+1) - A059305(n) - 1. - _Amiram Eldar_, May 14 2023
%e A176559 a(3) = 19 because between 3rd and fourth Mersenne primes (31 and 127) there are 19 primes (37, 41, 43, ... 113).
%t A176559 (* Run the program for A000668 first *) Table[-1 + PrimePi[A000668[[n + 1]]] - PrimePi[A000668[[n]]], {n, 7}] (* _Alonso del Arte_, Dec 07 2010 *)
%t A176559 PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[2^MersennePrimeExponent[Range[8]]-1,2,1]-1 (* The program generates the first 7 terms of the sequence. *) (* _Harvey P. Dale_, Jul 31 2025 *)
%Y A176559 Cf. A000040, A000668 (Mersenne primes), A059305.
%K A176559 nonn,hard,more
%O A176559 1,2
%A A176559 _G. L. Honaker, Jr._, Dec 07 2010
%E A176559 a(9) from the data at A059305 added by _Amiram Eldar_, May 14 2023