A128346 Numbers k such that (9^k - 5^k)/4 is prime.

3, 11, 17, 173, 839, 971, 40867, 45821, 147503

Offset: 1

Author

Alexander Adamchuk, Feb 27 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(9) > 10^5. - Robert Price, Jan 19 2013

a(10) > 10^6. - Jon Grantham, Jul 29 2023

Links

• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Crossrefs

Cf. A062572, A128344, A128345, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

Cf. A004061, A082182, A121877, A059802.

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

Programs

Mathematica

k=9; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

PARI

is(n)=isprime((9^n-5^n)/4) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7)-a(8) from Robert Price, Jan 19 2013

a(8) corrected by Robert Price, Jan 20 2013

a(9) from Jon Grantham, Jul 29 2023