%I #9 May 07 2012 23:55:55

%S 2,7,17,19,53,373,983,6709,6761,6763,17333,17707,43783,103681,317789,

%T 785671,2177321,5581493,38770357,39070457,1836305137,10749957121,

%U 12586147631,12586251313,32951279111,86252640919,86267571127,86267571263,213265164691,225845730829

%N Primes with equal number of 1's and 0's in their representation in base of Fibonacci numbers (A014417).

%e Representation of 19 is 101001, three 1's and three 0's, so 19 is in the sequence.

%e Representation of 23 is 1000010, two 1's and five 0's, so 23 is not in the sequence.

%t nn = 30; f = Join[{0}, Accumulate[Fibonacci[Range[2, 2*nn, 2] - 1]]]; t = Table[hi = f[[n+1]] - 1; Reverse[Table[hi - f[[i]], {i, n - 1}]], {n, 2, nn}]; Select[Flatten[t], PrimeQ] (* _T. D. Noe_, May 07 2012 *)

%Y Cf. A003714, A014417, A000045, A000040.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, May 05 2012

%E Extended by _T. D. Noe_, May 07 2012