A115596 The least number k > 1 such that (p+1)^k - p^k is prime, p = n-th prime.

2, 2, 2, 7, 2, 3, 3, 5, 2, 2, 5, 3, 2, 37, 58543, 2, 4663, 17, 3, 61, 23, 7, 2, 2, 7, 5, 7, 59, 5, 2, 59, 2, 196873

Offset: 1

Author

Zak Seidov, Jan 25 2006

Keywords

• nonn
• more

Comments

Values k=1 is omitted as in this case p is Sophie Germain prime (2p+1 is also prime) A005384.

Each term is necessarily prime. Sophie Germain primes correspond to case k = 2. - Giuseppe Coppoletta, Oct 10 2018

Examples

			a(1)=2 because (2+1)^2-2^2 = 5 is prime;
a(14)=37 because p(14)=43 and (43+1)^37-43^37 = 3679488080703419029992001830200360494989758810080014618823621 is prime.
		

Crossrefs

Cf. A005384, A058013.

Programs

Mathematica

s={}; Do[n=Prime[i];k=2; While[!PrimeQ[(n+1)^k-n^k],k++]; AppendTo[s, k],  {i, 14}]; s (* Amiram Eldar, Oct 12 2018 *)

PARI

a(n)=my(p=prime(n),k=1); while(!ispseudoprime((p+1)^k++-p^k),); k \\ Charles R Greathouse IV, Oct 08 2013

Extensions

Edited by Giuseppe Coppoletta, Oct 10 2018

a(15)-a(33) from Vaclav Kotesovec, Oct 11 2018