A236167 Numbers k such that (47^k + 1)/48 is prime.

5, 19, 23, 79, 1783, 7681

Offset: 1

Author

Robert Price, Jan 19 2014

Keywords

• hard
• more
• nonn

Comments

a(7) > 10^5.

Links

• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
• H. Lifchitz, Mersenne and Fermat primes field.
• Eric Weisstein's World of Mathematics, Repunit.

Crossrefs

Cf. A000978 = numbers k such that (2^k + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604, A231865, A235683.

Programs

Mathematica

Do[ p=Prime[n]; If[ PrimeQ[ (47^p + 1)/48 ], Print[p] ], {n, 1, 9592} ]

PARI

is(n)=ispseudoprime((47^n+1)/48) \\ Charles R Greathouse IV, Jun 06 2017

Python

from sympy import isprime
def afind(startat=0, limit=10**9):
  pow47 = 47**startat
  for k in range(startat, limit+1):
    q, r = divmod(pow47+1, 48)
    if r == 0 and isprime(q): print(k, end=", ")
    pow47 *= 47
afind(limit=300) # Michael S. Branicky, May 19 2021