A128030 Numbers k such that (16^k - 3^k)/13 is prime.

2, 3, 31, 467, 1747, 29683

Offset: 1

Author

Alexander Adamchuk, Feb 11 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

No other terms < 100000.

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, A128026, A128027, A128028, A128029, A128031, A128032.

Programs

Mathematica

k=13; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

PARI

is(n)=isprime((16^n-3^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

1747 from Farideh Firoozbakht, Apr 08 2007

a(6)=29683 from Robert Price, Sep 13 2011