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A128024
Numbers k such that (7^k - 3^k)/4 is prime.
30
3, 7, 19, 109, 131, 607, 863, 2917, 5923, 12421, 187507, 353501, 817519
OFFSET
1,1
COMMENTS
All terms are primes. No other terms < 1000000.
LINKS
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.
MATHEMATICA
k=4; Select[ Prime[ Range[1, 200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
PROG
(PARI) forprime(p=3, 1e5, if(ispseudoprime((7^p-3^p)/4), print1(p", "))) \\ Charles R Greathouse IV, Jun 01 2011
(Python)
from sympy import isprime
def aupto(lim): return [k for k in range(lim+1) if isprime((7**k-3**k)//4)]
print(aupto(900)) # Michael S. Branicky, Mar 07 2021
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 11 2007
EXTENSIONS
a(8)-a(9) from Farideh Firoozbakht, Apr 08 2007
a(10) from Robert Price, Jun 01 2011
a(11)-a(13) from Jon Grantham, Jul 29 2023
STATUS
approved