A253271 Decimal expansion of Sum{r^(-2^k), k >= 0}, where r = golden ratio.

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

Offset

1,3

Links

Table of n, a(n) for n=1..86.

Formula

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

Example

1.167637579159452929183950302006670871756901438...
First 4 terms: 1/r + 1/r^2 + 1/r^4 + 1/r^8.

Mathematica

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

Prog

(PARI) suminf(x=0, ((sqrt(5)+1)/2)^(-2^x)) \\ Michel Marcus, May 02 2015

Crossrefs

Cf. A000045, A001622 (golden ratio).

Sequence in context: A239134 A196616 A369104 * A258945 A120962 A355922

Adjacent sequences: A253268 A253269 A253270 * A253272 A253273 A253274

Keyword

nonn,cons,easy

Author

Clark Kimberling, May 01 2015

Status

approved