A128069 Numbers k such that (3^k + 10^k)/13 is prime.

3, 19, 31, 101, 139, 167, 1097, 43151, 60703, 90499

Offset: 1

Author

Alexander Adamchuk, Feb 14 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

Next term is greater than 6700. - Stefan Steinerberger, May 11 2007

a(11) > 10^5. - Robert Price, Jan 15 2013

Crossrefs

Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128070, A128071, A128072, A128073, A128074, A128075. 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, A128030, A128031, A128032.

Programs

Mathematica

k=10; 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+10^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(7) from Alexander Adamchuk, Feb 14 2007

a(8)-a(10) from Robert Price, Jan 15 2013