A173718 Numbers n such that (9^n - 2^n)/7 is prime.

2, 3, 5, 13, 29, 37, 1021, 1399, 2137, 4493, 5521, 108553, 200807

Offset: 1

Author

Robert Price, Dec 22 2012

Keywords

• hard
• more
• nonn

Comments

All terms are prime.

a(14) > 10^6.

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. A004063, A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

Mathematica

Select[ Prime[ Range[1, 100000] ], PrimeQ[ (9^# - 2^#)/7 ]& ]

PARI

is(n)=ispseudoprime((9^n-2^n)/7) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

a(12)-a(13) from Jon Grantham, Jul 29 2023