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A236167
Numbers k such that (47^k + 1)/48 is prime.
2
5, 19, 23, 79, 1783, 7681
OFFSET
1,1
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.
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
Do[ p=Prime[n]; If[ PrimeQ[ (47^p + 1)/48 ], Print[p] ], {n, 1, 9592} ]
PROG
(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
KEYWORD
hard,more,nonn
AUTHOR
Robert Price, Jan 19 2014
STATUS
approved