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 A134775 #28 Jun 26 2025 06:43:51
%S A134775 2,9,11,31,46,146,795,2773,2788,9797,38289,39192,40857,41203,47380
%N A134775 Numbers k such that the sum of first k Catalan numbers is a prime.
%C A134775 Corresponding primes are listed in A134776. A134776(n) = A014138(a(n)-1).
%C A134775 a(16) > 156000. - _Michael S. Branicky_, Jun 26 2025
%H A134775 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>
%F A134775 a(n) = A126807(n) + 1. - _Michael S. Branicky_, Jun 24 2025
%e A134775 a(1) = 2 because C(1) + C(2) = 1 + 2 = 3 is a prime.
%e A134775 a(2) = 9 because C(1) + C(2) + C(3) + C(4) + C(5) + C(6) + C(7) + C(8) + C(9) = 1 + 2 + 5 + 14 + 42 + 132 + 429 + 1430 + 4862 = 6917 is a prime.
%p A134775 for n to 3000 do c[n]:= binomial(2*n,n)/(n+1) end do: a:=proc(n) if isprime(add(c[j],j=1..n))=true then n else end if end proc: seq(a(n),n=1..3000); # _Emeric Deutsch_, Nov 19 2007
%t A134775 f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} ] ], {n, 1, 1000} ]
%t A134775 Flatten[Position[Accumulate[CatalanNumber[Range[1000]]],_?PrimeQ]] (* _Harvey P. Dale_, Jan 28 2013 *)
%Y A134775 Cf. A134776 (primes that are the sum of first n Catalan numbers).
%Y A134775 Cf. A014138 (partial sums of Catalan numbers).
%Y A134775 Cf. A000108 (Catalan numbers).
%Y A134775 Cf. A126807.
%K A134775 hard,more,nonn
%O A134775 1,1
%A A134775 _Alexander Adamchuk_, Nov 11 2007
%E A134775 a(8)-a(9) from _Emeric Deutsch_, Nov 19 2007
%E A134775 a(10) from _Ryan Propper_, Jan 06 2008
%E A134775 a(11)-a(15) from _Michael S. Branicky_, Jun 25 2025