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

%I A236167 #20 Feb 16 2025 08:33:21
%S A236167 5,19,23,79,1783,7681
%N A236167 Numbers k such that (47^k + 1)/48 is prime.
%C A236167 a(7) > 10^5.
%H A236167 J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
%H A236167 H. Dubner and T. Granlund, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/DUBNER/dubner.html">Primes of the Form (b^n+1)/(b+1)</a>, J. Integer Sequences, 3 (2000), #P00.2.7.
%H A236167 H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>.
%H A236167 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>.
%t A236167 Do[ p=Prime[n]; If[ PrimeQ[ (47^p + 1)/48 ], Print[p] ], {n, 1, 9592} ]
%o A236167 (PARI) is(n)=ispseudoprime((47^n+1)/48) \\ _Charles R Greathouse IV_, Jun 06 2017
%o A236167 (Python)
%o A236167 from sympy import isprime
%o A236167 def afind(startat=0, limit=10**9):
%o A236167   pow47 = 47**startat
%o A236167   for k in range(startat, limit+1):
%o A236167     q, r = divmod(pow47+1, 48)
%o A236167     if r == 0 and isprime(q): print(k, end=", ")
%o A236167     pow47 *= 47
%o A236167 afind(limit=300) # _Michael S. Branicky_, May 19 2021
%Y A236167 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.
%K A236167 hard,more,nonn
%O A236167 1,1
%A A236167 _Robert Price_, Jan 19 2014