Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #35 Aug 15 2023 02:17:47
%S 2,1,1,2,1,2,1,2,3,18,1,2,1,2,3,6,1,2,1,2,41,110,1,18,3,2,11,2,1,24,1,
%T 2,3,2,107827,2,1,8,3,24,1,2,1,514,6737,2,1,2,5521,140,15,108,1,2,15,
%U 82,35
%N Smallest k such that n^k - k is a prime, or 0 if no such number exists.
%C Conjecture: no entry is zero.
%C If n is odd and greater than 3, k=a(n) is even. If n is an even composite number, k=a(n) is odd. For n>2, n and k=a(n) are coprime. - _R. J. Mathar_, Apr 02 2006, corrected by _Farideh Firoozbakht_, Aug 09 2014
%C a(36)>30000 or 0. a(37)..a(46) = 2, 1, 8, 3, 24, 1, 2, 1, 514, 6737. - _Max Alekseyev_, Apr 24 2009
%C If n-1 is prime then a(n)=1. - _Farideh Firoozbakht_, Aug 09 2014
%H Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=36%5E107827%2D107827">36^107827-107827</a>, a(36).
%p a := proc(n) local k; k := 1; while not isprime(n^k-k) do k := k+1 od; k end: seq(a(n),n=2..35);
%t f[n_] := Block[{k = 1}, If[OddQ[n], k++ ]; While[ ! PrimeQ[n^k - k], k += 2]; k]; Table[ f[n], {n, 3, 35}]
%Y Cf. A084745.
%K more,nonn,hard
%O 2,1
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003
%E Edited and extended by _Robert G. Wilson v_, Alec Mihailovs (Alec(AT)Mihailovs.com) and _T. D. Noe_, Jun 16 2003
%E a(36)-a(58) from _Kellen Shenton_, Aug 14 2023