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 A058077 #53 Feb 16 2024 10:13:27
%S A058077 3,10,21,330,78,2380,171,8855,475020,465,2324784,101270,903,178365,
%T A058077 22957480,45057474,1830,99795696,971635,2628,277962685,1837620,
%U A058077 581106988,144520208820,4082925,5253,5160610,5886,6438740
%N A058077 Binomial coefficients formed from consecutive primes: a(n) = binomial( prime(n+1), prime(n) ).
%C A058077 Conjecture: for each value of n > 1, if a(n+1) has the same number of digits as a(n) and a(n+1) > a(n), then prime(n+2) - prime(n+1) = prime(n+1) - prime(n). This conjecture has been verified for all n < 3*10^7. - _Ahmad J. Masad_, Oct 08 2019
%H A058077 Michel Marcus, <a href="/A058077/b058077.txt">Table of n, a(n) for n = 1..10000</a>
%H A058077 Rémy Sigrist, <a href="/A058077/a058077.png">Colored logarithmic scatterplot of the first 100000 terms</a> (where the color is function of A001223(n))
%F A058077 a(n) = binomial(A000040(n+1), A001223(n)).
%e A058077 n=6: a(6) = C(p(7),p(6)) = C(17,13) = 57120/24 = 2380.
%t A058077 Table[Binomial[Prime[n+1],Prime[n]],{n,1,20}] (* _Vaclav Kotesovec_, Nov 13 2014 *)
%Y A058077 Cf. A000040, A001223.
%Y A058077 Cf. A037293, A066526, A080911, A277341.
%K A058077 nonn
%O A058077 1,1
%A A058077 _Labos Elemer_, Nov 13 2000
%E A058077 Offset corrected by _Vaclav Kotesovec_, Nov 13 2014