A305738 Numbers k such that k!*T(k) - 1 is prime, where T(k) is the k-th triangular number.

2, 4, 28, 34, 47, 62, 228, 256, 258, 341, 848, 1362, 1709, 2262, 2692, 7907, 10396, 10501

Offset: 1

Author

Maheswara Rao Valluri, Jun 22 2018

Keywords

• nonn
• more

Comments

The PFGW program has been used to certify all the terms up to a(18), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Jun 24 2018

Links

• Maheswara Rao Valluri, Primes of the form p = 1 + n! Sum n, for some n ∈ N*, arXiv:1803.11461 [math.GM], 2018.

Crossrefs

Cf. A302859, A301373.

Programs

Mathematica

Do[If[ PrimeQ[n(n +1)!/2 - 1], Print@ n], {n, 3000}]

PARI

isok(n) = ispseudoprime(n(n+1)!/ 2 - 1);

Extensions

a(16)-a(18) from Giovanni Resta, Jun 24 2018