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

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

Offset: 1

Author

Alexander Adamchuk, Feb 11 2007

Keywords

• hard
• nonn

Comments

All terms are primes.

No other terms < 1000000.

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. 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.

Programs

Mathematica

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

PARI

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

Extensions

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

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