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A253271
Decimal expansion of Sum_{k>=0} r^(-2^k), where r = golden ratio.
0
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
FORMULA
Equals Sum_{k>=0} 1/(F(2^k-1) + r*F(2^k)), 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
KEYWORD
nonn,cons,easy,changed
AUTHOR
Clark Kimberling, May 01 2015
STATUS
approved