1,1

A078202[n] is the smallest prime of the form abs(n^k - k^n), the absolute difference between n^k and k^n, or -1 if no such prime exists. A078202[n] = {2, 7, 2, 3, 7, 5, 79, 7, 431, 58049, 8375575711, 11, 13055867207, 13, 94233563770233419658037661865757455268745312881861761180195872329157714108064193, -1, 130783, 17, ...}. a(n) = -1 for n = {16,64,...} when A078202[n] = -1. a(n) = 1 for n = {3,4,6,8,12,14,18,20,...} = A008864[n] Primes + 1, when A078202[p+1] = p. Currently a(n) is not known for n = {22,27,28,33,36,37,39,40,46,55,56,57,59,...}. a(23)-a(26) = {60,1,12,5}. a(29)-a(32) = {98,1,42,1}. a(34)-a(35) = {69,6}. a(38) = 1. a(41)-a(45) = {60,1,32,1,44}. a(47)-a(54) = {110,1,24,9,2,3,2,1}. a(58) = 93. a(60)-a(64) = {1,180,1,88,-1}.

f[n_] := Block[{k = If[EvenQ@n || n < 4, 1, 2]}; While[ ! PrimeQ@Abs[n^k - k^n], k += 2]; k] (* Robert G. Wilson v *)

Cf. A078202, A008864, A122735.

Sequence in context: A091717 A154512 A030588 this_sequence A074903 A143303 A091084

Adjacent sequences: A123698 A123699 A123700 this_sequence A123702 A123703 A123704

hard,more,sign

Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 08 2006