A383476 Numbers k such that binomial(2k,k) + k is prime.

1, 3, 5, 23, 55, 61, 191, 1933, 3049, 8011, 10589, 58687, 100469

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 28 2025

Keywords

• nonn
• hard
• more

Comments

Corresponding primes start 3, 23, 257, 8233430727623, 98527218530093856775578873054487.

Crossrefs

Cf. A134758, A309289.

Programs

Magma

[k: k in [1..1000] | IsPrime(Binomial(2*k,k)+k)];

Mathematica

Select[Range[3500], PrimeQ[Binomial[2*#, #] + #] &] (* Amiram Eldar, Apr 28 2025 *)

Python

from math import comb
from gmpy2 import is_prime
def ok(n): return is_prime(comb(2*n, n) + n)
print([k for k in range(3050) if ok(k)]) # Michael S. Branicky, Apr 28 2025

Extensions

a(7) inserted and a(10)-a(13) from Michael S. Branicky, Apr 29 2025