A128026 Numbers n such that (10^n - 3^n)/7 is prime.

2, 3, 5, 37, 599, 38393, 51431, 118681, 376417

Offset

1,1

Comments

All terms are primes.

No other terms < 1000000.

Links

Table of n, a(n) for n=1..9.

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

Mathematica

k=7; Select[ Prime[ Range[1, 200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

Prog

(PARI) forprime(p=2, 1e4, if(ispseudoprime((10^p-3^p)/7), print1(p", "))) \\ Charles R Greathouse IV, Jun 05 2011

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, A128025, A128027, A128028, A128029, A128030, A128031, A128032.

Sequence in context: A089213 A029499 A347720 * A041443 A336787 A057775

Adjacent sequences: A128023 A128024 A128025 * A128027 A128028 A128029

Keyword

hard,nonn

Author

Alexander Adamchuk, Feb 11 2007

Extensions

a(6)-a(7) from Robert Price, Jun 04 2011

a(8)-a(9) from Jon Grantham, Jul 29 2023

Status

approved