A271718 -id:A271718 - cp's OEIS frontend

A191568 Numbers k such that k*(k+1)^k+1 is prime.

1, 2, 3, 9, 10, 14, 33, 36

Offset: 1

Juri-Stepan Gerasimov, Jun 13 2011

The corresponding primes are a subset of the generalized Cullen primes (A210339 U A050920). - Jeppe Stig Nielsen, Apr 12 2016

			a(1)=1 because 1*2^1+1=3 is prime, a(2)=2 because 2*3^2+1=19 is prime, a(3)=3 because 3*4^3+1=193 is prime, a(4)=9 because 9*10^9+1=9000000001 is prime, a(5)=10 because 10*11^10+1=259374246011 is prime.

Cf. A109618, A110709, A210339, A271718.

Select[Range@ 100, PrimeQ[# (# + 1)^# + 1] &] (* Michael De Vlieger, Apr 12 2016 *)

is(n)=ispseudoprime(n*(n+1)^n+1) \\ Charles R Greathouse IV, Jun 13 2017

A353122 Numbers k such that k^k*(k+1) + 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 186, 198, 8390

Offset: 1

Juri-Stepan Gerasimov, Apr 24 2022

Corresponding primes start 2, 3, 13, 109, 326593, 3874204891, ...
a(9) > 6000. - Jon E. Schoenfield, Jun 05 2022
a(10) > 18000. - Michael S. Branicky, Aug 08 2024

			9 is in the sequence because 9^9*(9+1) + 1 = 3874204891, which is prime.

Cf. A055897, A081132, A108318, A108879, A191513, A191568, A271718.

[n: n in [0..200] | IsPrime(n^n*(n+1) + 1)];

Join[{0}, Select[Range[200], PrimeQ[#^#*(# + 1) + 1] &]] (* Amiram Eldar, Apr 25 2022 *)

isok(k) = ispseudoprime(k^k*(k+1) + 1); \\ Michel Marcus, May 16 2022

a(9) from Michael S. Branicky, Dec 22 2023

cp's OEIS Frontend

A191568 Numbers k such that k*(k+1)^k+1 is prime.

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