A128029 Numbers n such that (14^n - 3^n)/11 is prime.

2, 5, 13, 67, 2657, 3547, 15649

Offset: 1

Author

Alexander Adamchuk, Feb 11 2007

Keywords

• hard
• nonn

Comments

All terms are primes.

There is no further term up to prime(1400)=11657. - Farideh Firoozbakht, Apr 04 2007

No other terms < 100,000.

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, A128030, A128031, A128032.

Programs

Mathematica

k=11; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]

PARI

is(n)=isprime((14^n-3^n)/11) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Farideh Firoozbakht, Apr 04 2007

Added term a(7)=15649 by Robert Price, Sep 12 2011