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 A125220 #22 May 26 2025 06:48:13
%S A125220 1,3,7,11,49,88,93,196,216,519,655,722,858,905,991,1654,2277,3275,
%T A125220 4214,5047,5924,7359,7953,11188,13286,14626,14687,34365,36014,65613,
%U A125220 93663,101805
%N A125220 Numbers k such that binomial(3k, k) - 1 is prime.
%t A125220 Do[f=Binomial[3n, n]-1; If[PrimeQ[f], Print[n]], {n, 1, 1000}]
%t A125220 Select[Range[4300],PrimeQ[Binomial[3#,#]-1]&] (* _Harvey P. Dale_, Aug 24 2017 *)
%o A125220 (PARI) is(n)=binomial(3*n,n)-1 \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A125220 Cf. A125221 (binomial(3k, k) + 1 is prime).
%Y A125220 Cf. A066699 (binomial(2k, k) + 1 is prime).
%Y A125220 Cf. A066726 (binomial(2k, k) - 1 is prime).
%K A125220 hard,more,nonn
%O A125220 1,2
%A A125220 _Alexander Adamchuk_, Nov 25 2006
%E A125220 a(16)-a(19) from _Robert G. Wilson v_, Nov 26 2006
%E A125220 a(20)-a(29) from _Robert Price_, Apr 23 2019
%E A125220 a(30)-a(32) from _Georg Grasegger_, May 26 2025