login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that (29^k - 2^k)/27 is prime.
0

%I #5 Sep 24 2024 06:21:03

%S 2,7,139,983,3257,10181,26387,36187,42557

%N Numbers k such that (29^k - 2^k)/27 is prime.

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

%C a(10) > 10^5.

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

%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 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[1000]], PrimeQ[(29^# - 2^#)/27] &]

%Y Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236.

%K nonn,hard,more

%O 1,1

%A _Robert Price_, Sep 24 2024