A253271 - OEIS

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

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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]]