A265483 Numbers k such that 25^k - 5^k - 1 is prime.

1, 2, 4, 15, 16, 24, 57, 206, 284, 1290, 1722, 1862, 1866, 3271, 5306, 5474, 15401, 18729, 34757, 42842, 63930, 89967

Offset: 1

Author

Vincenzo Librandi, Dec 11 2015

Keywords

• nonn
• more

Comments

For k = 1, 2, 4, 15, 16, the corresponding primes are 19, 599, 389999, 931322574584960937499, 23283064365234374999999.

a(n) is not of the form 5*m + 3 (divisibility by 11) or 9*m + 10 (divisibility by 19), 7*m + (-1)^m + 7 (divisibility by 29) or 29*m + 27 (divisibility by 59).

a(23) > 10^5. - Robert Price, Dec 12 2019

Examples

			4 is in the sequence because 25^4-5^4-1 = 389999 is prime.
		

Crossrefs

Cf. similar sequences listed in A265481.

Programs

Magma

[n: n in [0..300] | IsPrime(25^n-5^n-1)];

Mathematica

Select[Range[6000], PrimeQ[25^# - 5^# - 1] &]

PARI

is(n)=ispseudoprime(25^n - 5^n - 1) \\ Anders Hellström, Dec 11 2015

Extensions

a(17)-a(22) from Robert Price, Dec 12 2019