A265487 Numbers k such that 81^k - 9^k - 1 is prime.

1, 3, 10, 18, 70, 585, 921, 1943, 4635, 13543, 13803, 15938, 39004

Offset: 1

Author

Vincenzo Librandi, Dec 12 2015

Keywords

• nonn
• more

Comments

2*a(n) is in A265481.

For k = 1, 3, 10, 18 the corresponding primes are 71, 530711, 12157665455570144399, 22528399544939174261745512577773519.

a(n) is not of the form 5*k+2 (divisibility by 11), 9*k+2 (divisibility by 19), 7*k+2*(-1)^k+7 (divisibility by 29), 15*k+2 (divisibility by 31) or 29*k+8 (divisibility by 59).

a(14) > 10^5. - Robert Price, Apr 21 2020

Examples

			3 is in the sequence because 81^3 - 9^3 - 1 = 530711 is prime.
		

Crossrefs

Cf. similar sequences listed in A265481.

Programs

Magma

[n: n in [0..500] | IsPrime(81^n-9^n-1)];

Mathematica

Select[Range[1000], PrimeQ[81^# - 9^# - 1] &]

PARI

for(n=1, 1e3, if(ispseudoprime(81^n - 9^n - 1), print1(n, ", "))) \\ Altug Alkan, Dec 12 2015

Extensions

a(9) from Altug Alkan, Dec 12 2015

a(10)-a(13) computed from A265481 by Ray Chandler, Sep 25 2019