%I #14 May 02 2015 10:10:13

%S 1,1,6,7,6,3,7,5,7,9,1,5,9,4,5,2,9,2,9,1,8,3,9,5,0,3,0,2,0,0,6,6,7,0,

%T 8,7,1,7,5,6,9,0,1,4,3,8,8,4,0,8,8,1,7,0,2,2,1,1,0,1,3,0,5,8,0,6,0,8,

%U 8,7,1,5,6,5,3,7,5,0,8,0,1,1,0,5,7,8

%N Decimal expansion of Sum{r^(-2^k), k >= 0}, where r = golden ratio.

%F Sum{1/[F(2^n-1) + r*F(2^n)], k >= 0, where r = golden ratio and F = A000045 (Fibonacci numbers).

%e 1.167637579159452929183950302006670871756901438...

%e First 4 terms: 1/r + 1/r^2 + 1/r^4 + 1/r^8.

%t RealDigits[N[Sum[GoldenRatio^(-2^k), {k, 0, 25}], 130]][[1]]

%o (PARI) suminf(x=0, ((sqrt(5)+1)/2)^(-2^x)) \\ _Michel Marcus_, May 02 2015

%Y Cf. A000045, A001622 (golden ratio).

%K nonn,cons,easy

%O 1,3

%A _Clark Kimberling_, May 01 2015