%N Nonprimes which are the average of two consecutive Fibonacci numbers.
%C Prove that 17 is the only prime which is the average of two consecutive Fibonacci numbers.
%t f[n_] := Fibonacci[n]; a = Select[ Range, IntegerQ[(f[ # ] + f[ # + 1])/2] && !PrimeQ[(f[ # ] + f[ # + 1])/2] &]; (f[a] + f[a + 1])/2
%Y Cf. A018252, A000045.
%A _G. L. Honaker, Jr._, Jun 22 2002
%E Edited by _Robert G. Wilson v_, Jun 27 2002