A273403 Numbers k such that (10^k - 7^k)/3 is prime.

2, 31, 103, 617, 10253, 10691, 35353, 129587, 556441

Offset: 1

Author

Tim Johannes Ohrtmann, May 21 2016

Keywords

• nonn
• more
• hard

Comments

All terms are prime.

The corresponding primes: 17, 3333280741539321718064461652419, ...

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. A004023, A128026, A062576.

Programs

Mathematica

Select[Range[1, 10000], PrimeQ[(10^# - 7^#)/3] &]

PARI

for(n=1, 10000, if(isprime((10^n - 7^n)/3), print1(n, ", ")))

Extensions

a(7)-a(9) from Jon Grantham, Jul 29 2023