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A236167
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Numbers k such that (47^k + 1)/48 is prime.
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2
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OFFSET
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1,1
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COMMENTS
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a(7) > 10^5.
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
Eric Weisstein's World of Mathematics, Repunit.
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MATHEMATICA
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Do[ p=Prime[n]; If[ PrimeQ[ (47^p + 1)/48 ], Print[p] ], {n, 1, 9592} ]
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PROG
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(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
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CROSSREFS
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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.
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KEYWORD
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hard,more,nonn
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AUTHOR
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STATUS
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approved
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