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Numbers k such that (23^k - 2^k)/21 is prime.
13

%I #26 Aug 06 2024 14:16:37

%S 5,11,197,4159

%N Numbers k such that (23^k - 2^k)/21 is prime.

%C The definition implies that k must be a prime.

%C a(5) > 10^5.

%H 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 P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>

%H 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 H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>.

%t Select[Prime[Range[100]], PrimeQ[(23^# - 2^#)/21] &]

%Y Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542.

%K nonn,hard,more

%O 1,1

%A _Robert Price_, Aug 04 2024