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 A335889 #29 Jul 20 2020 08:32:57
%S A335889 1,2,0,3,1,0,0,3,1,0,0,2,0,3,2,1,0,0,0,3,0,2,1,0,1,1,2,1,0,0,4,0,0,0,
%T A335889 2,0,2,3,3
%N A335889 a(n) is the number of Mersenne primes between consecutive perfect numbers.
%H A335889 Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?curio_id=38700">Prime Curio for 756839</a>
%e A335889 a(1) = 1 because there is exactly 1 Mersenne prime (7) between the first and second perfect numbers (6 and 28).
%e A335889 a(4) = 3 because there are exactly 3 Mersenne primes (8191, 131071, 524287) between the fourth and fifth perfect numbers (8128 and 33550336).
%t A335889 p = MersennePrimeExponent @ Range[47];mer[p_] := 2^p - 1; perf[p_] := mer[p] * 2^(p - 1); mers = mer /@ p; perfs = Select[perf /@ p, # < mers[[-1]] &]; BinCounts[mers, {perfs}] (* _Amiram Eldar_, Jun 29 2020 *)
%Y A335889 Cf. A000043, A000396, A000668.
%K A335889 nonn,more
%O A335889 1,2
%A A335889 _G. L. Honaker, Jr._, Jun 28 2020
%E A335889 a(5)-a(13) from _Metin Sariyar_, Jun 28 2020
%E A335889 a(14)-a(16) and a(20)-a(39) from _Metin Sariyar_, Jun 29 2020
%E A335889 a(17)-a(19) from _Amiram Eldar_, Jun 29 2020