A210339 -id:A210339 - cp's OEIS frontend

A246809 Composite numbers such that n^(b^n) == (-1)^b (mod C_b(n)), where C_b(n) = n*b^n+1 (A210339).

Original entry on oeis.org

12801, 136497879001, 422240040001, 18677955240001

Offset: 1

Felix Fröhlich, Nov 16 2014

J. M. Grau and A. M. Oller-Marcen, An O(log^2(N)) time primality test for generalized Cullen numbers, Math. Comp., Vol. 80, Num. 276 (2011), 2315-2323.

Cf. A210339.

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

Original entry on oeis.org

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

A295052 Smallest b > n+2 such that n*b^n + 1 is a generalized Cullen prime with n > 1 and base b > n+2 or 0 if no such prime exists.

Original entry on oeis.org

6, 10, 0, 8, 14, 30, 12, 14, 132, 42, 143, 60, 30, 22, 170, 30, 665, 198, 42, 200, 138, 104, 115, 34, 84, 0, 1740, 54, 403, 130, 150, 134, 58, 72, 111, 778, 204, 174, 1681, 108, 344, 178, 585, 86, 7426, 904, 133, 234, 63, 1376, 114, 108

Offset: 2

Pierre CAMI, Nov 13 2017

nonn

No prime found for n = 4, 27, 64.

Record values: a(3)=10, a(7)=30, a(10)=132, a(12)=143, a(16)=170, a(18)=665, a(28)=1740, a(46)=7426, a(66)=19899, a(100)=21412, a(112)=52601.

Cf. A210339.

cp's OEIS Frontend

A246809 Composite numbers such that n^(b^n) == (-1)^b (mod C_b(n)), where C_b(n) = n*b^n+1 (A210339).

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

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A295052 Smallest b > n+2 such that n*b^n + 1 is a generalized Cullen prime with n > 1 and base b > n+2 or 0 if no such prime exists.

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