A187602 Primes of the form (k+1)^(k-1) + k.

2, 5, 19, 1301, 262151, 4782977

Offset: 1

Author

Marco Ripà, Mar 11 2011

Keywords

• nonn
• hard

Comments

The next terms are too large to be displayed:

a(7) = 159^157 + 158 (k = 158), which is 346 digits long.

a(8) = 537^535 + 536 (k = 536), which is 1461 digits long.

a(9) = 4671^4669 + 4670 (k = 4670), which is 17133 digits long.

a(10) = 9796^9794 + 9795 (k = 9795), which is 39089 digits long.

Next term has k >= 30000.

Examples

			1301 is in the sequence since it is prime and, using k = 5, (k+1)^(k-1) + k = 6^4 + 5 = 1296 + 5 = 1301.
		

Crossrefs

Cf. A238378 (corresponding k).

Programs

Mathematica

Do[p=(n+1)^(n-1)+n; If[PrimeQ[p], Print[p]], {n, 250}]

PARI

lista(nn) = for(k=1, nn, if(ispseudoprime(q=(k+1)^(k-1)+k), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020

Extensions

a(8)-a(10) from Matevz Markovic, Mar 03 2014