A128025 Numbers k such that (8^k - 3^k)/5 is prime.

2, 3, 7, 19, 31, 67, 89, 9227, 43891, 854149

Offset

1,1

Comments

All terms are primes.

Verified the first 8 terms in sequence. Also, the next number in the sequence, if one exists is > 43691. - Robert Price, Mar 16 2010

a(10) > 10^5. - Robert Price, Jul 27 2011

a(11) > 10^6. - Jon Grantham, Jul 29 2023

Links

Table of n, a(n) for n=1..10.

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

Mathematica

k=5; Select[ Prime[ Range[1, 200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

Prog

(PARI) is(n)=isprime((8^n-3^n)/5) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Sequence in context: A195354 A244638 A113165 * A092064 A152609 A298943

Adjacent sequences: A128022 A128023 A128024 * A128026 A128027 A128028

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Feb 11 2007

Extensions

9227 from Farideh Firoozbakht, Apr 08 2007

a(9) from Robert Price, Jul 27 2011

a(10) from Jon Grantham, Jul 29 2023

Status

approved