%I A084746
%S A084746 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,
               2,
%T A084746 3,2
%N A084746 Smallest k such that n^k - k is a prime, or 0 if no such number exists.
%C A084746 Conjecture: no entry is zero.
%C A084746 If n is odd, k=a(n) is even. If n is even, k=a(n) is odd. n and k=a(n) 
               are coprime. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 
               2006
%C A084746 a(36)>30000 or 0. a(37)..a(46) = 2, 1, 8, 3, 24, 1, 2, 1, 514, 6737.
%p A084746 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 A084746 f[n_] := Block[{k = 1}, If[OddQ[n], k++ ]; While[ ! PrimeQ[n^k - k], 
               k += 2]; k]; Table[ f[n], {n, 3, 35}]
%Y A084746 Cf. A084745.
%Y A084746 Sequence in context: A053574 A065203 A029396 this_sequence A128259 A051194 
               A134838
%Y A084746 Adjacent sequences: A084743 A084744 A084745 this_sequence A084747 A084748 
               A084749
%K A084746 more,nonn
%O A084746 2,1
%A A084746 Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), 
               Jun 15 2003
%E A084746 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Alec Mihailovs 
               (Alec(AT)Mihailovs.com) and T. D. Noe (noe(AT)sspectra.com), Jun 
               16 2003.
%E A084746 Update on a(36) and a(46) from Max Alekseyev (maxale(AT)gmail.com), Apr 
               24 2009