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 A126807 #24 Jun 26 2025 06:42:53
%S A126807 1,8,10,30,45,145,794,2772,2787,9796,38288,39191,40856,41202,47379
%N A126807 Numbers k such that A014138(k+1) (the partial sum of the first k Catalan numbers, starting 1, 2, 5, ...) is a prime.
%C A126807 a(16) > 156000. - _Michael S. Branicky_, Jun 26 2025
%F A126807 a(n) = A134775(n) - 1. - _Michael S. Branicky_, Jun 24 2025
%p A126807 s[0]:=1: for n to 1000 do s[n]:= s[n-1]+binomial(2*n+2, n+1)/(n+2) end do: a:= proc (n) if isprime(s[n]) = true then n else end if end proc: seq(a(n), n= 0.. 1000); # _Emeric Deutsch_, Aug 28 2007
%t A126807 s = 0; Do[s = s + (2n)!/n!/(n+1)!; If[ PrimeQ[s], Print[n-1]], {n, 200}]
%Y A126807 Cf. A014138, A000108, A134775.
%Y A126807 Cf. A014137, A121852 (sum of first k Catalan numbers A014137(k) is prime).
%K A126807 more,nonn
%O A126807 1,2
%A A126807 _Alexander Adamchuk_, Feb 23 2007
%E A126807 a(7)-a(9) from _Emeric Deutsch_, Aug 28 2007
%E A126807 Name clarified by _Jon E. Schoenfield_, Mar 25 2019
%E A126807 a(10)-a(15) from _Michael S. Branicky_, Jun 25 2025