|
%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
|
