A125956 Numbers k such that (2^k + 9^k)/11 is prime.

3, 7, 127, 283, 883, 1523, 4001

Offset: 1

Author

Alexander Adamchuk, Feb 06 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes. Note that first 3 terms {3, 7, 127} are primes of the form 2^q - 1, where q = {2, 3, 7} is prime too. Corresponding primes of the form (2^k + 9^k)/11 are {67, 434827, ...}.

a(8) > 10^5. - Robert Price, Dec 23 2012

Crossrefs

Cf. A000978 = numbers n such that (2^n + 1)/3 is prime.

Cf. A057469 = numbers n such that (2^n + 3^n)/5 is prime.

Cf. A082387 = numbers n such that (2^n + 5^n)/7 is prime.

Programs

Mathematica

Do[p=Prime[n];f=(2^p+9^p)/11; If[PrimeQ[f], Print[{p, f}]], {n, 1, 100}]

PARI

is(n)=ispseudoprime((2^n+9^n)/11) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

2 more terms from Rick L. Shepherd, Feb 14 2007

a(7) from Robert Price, Dec 23 2012