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 A383476 #19 May 04 2025 12:40:53 %S A383476 1,3,5,23,55,61,191,1933,3049,8011,10589,58687,100469 %N A383476 Numbers k such that binomial(2k,k) + k is prime. %C A383476 Corresponding primes start 3, 23, 257, 8233430727623, 98527218530093856775578873054487. %t A383476 Select[Range[3500], PrimeQ[Binomial[2*#, #] + #] &] (* _Amiram Eldar_, Apr 28 2025 *) %o A383476 (Magma) [k: k in [1..1000] | IsPrime(Binomial(2*k,k)+k)]; %o A383476 (Python) %o A383476 from math import comb %o A383476 from gmpy2 import is_prime %o A383476 def ok(n): return is_prime(comb(2*n, n) + n) %o A383476 print([k for k in range(3050) if ok(k)]) # _Michael S. Branicky_, Apr 28 2025 %Y A383476 Cf. A134758, A309289. %K A383476 nonn,hard,more %O A383476 1,2 %A A383476 _Juri-Stepan Gerasimov_, Apr 28 2025 %E A383476 a(7) inserted and a(10)-a(13) from _Michael S. Branicky_, Apr 29 2025