A128073 Numbers k such that (3^k + 16^k)/19 is prime.

5, 17, 61, 673, 919, 2089, 86939

Offset: 1

Author

Alexander Adamchuk, Feb 14 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

a(8) > 10^5 - Robert Price, Jun 29 2013

Crossrefs

Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).

Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).

Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).

Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128072, A128074, A128075.

Cf. A059801 (numbers k such that 4^k - 3^k is prime).

Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).

Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

Mathematica

k=16; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

PARI

is(n)=isprime((3^n+16^n)/19) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(5) from Alexander Adamchuk, Feb 14 2007

a(6) and a(7) from Robert Price, Jun 29 2013