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 A112861 #33 Jul 25 2024 14:02:59 %S A112861 2,6,10,21,45,63,306,404,437,471,646,1174,1192,1334,1975,2397,2410, %T A112861 4305,6111,7852,9488,11120,13304,14408,16075,16238,21188,21659,22025, %U A112861 28673,30793,32178,35278,40049,46516,47836,52157,54531,59897,60275,63362,76139,84219,89024,90783,91605,96761 %N A112861 Numbers k such that (2*k)!/(2*(k!)^2) - 1 is prime. %C A112861 a(48) > 100000. - _Robert Price_, Jul 25 2024 %t A112861 Select[Range[10000], PrimeQ[(2 #)! / (2 (#!)^2) - 1 ] &] (* _Vincenzo Librandi_, Apr 10 2015 *) %o A112861 (Magma) [n: n in [1..700] | IsPrime(Factorial(2*n) div (2*Factorial(n)^2)-1)]; // _Vincenzo Librandi_, Apr 10 2015 %Y A112861 Cf. A001700(n-1) = (2*n)!/(2*(n!)^2); A112862: primes of the form (2*n)!/(2*(n!)^2)-1; A112853: (2*n)!/n!-1 is prime; A112855: (2*n)!/n!+1 is prime; A066726: (2*n)!/(n!)^2-1 is prime; A066699: (2*n)!/(n!)^2+1 is prime; A112863: (2*n)!/(2*(n!)^2)+1 is prime. %K A112861 hard,nonn %O A112861 1,1 %A A112861 _Hugo Pfoertner_, Sep 30 2005 %E A112861 a(22)-a(26) from _Vaclav Kotesovec_, May 02 2021 %E A112861 a(27)-a(47) from _Robert Price_, Jul 25 2024