A249601 Decimal expansion of 1/phi + 1/phi^3 + 1/phi^5 + 1/phi^7, where phi is the Golden Ratio.

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

Offset

0,1

Comments

1/phi + 1/phi^3 + 1/phi^5 + 1/phi^7 + 1/phi^9 + ... = 1.

References

David Snook, Email, Mar 31 2009.

Links

Table of n, a(n) for n=0..93.

Formula

Equals phi^8 - 46 = phi/(1 + phi/(2 + phi/(3 + phi/(4 + phi/(12 + phi/(1 + phi/(1 + phi/(2 + phi/(7 + phi/(6 + phi/(1 + phi/(1 + phi/(2))))))))))))) = 21*sqrt(5)/2 - 45/2. - Peter Bala, Dec 30 2025

Maple

3*(7*sqrt(5)-15)/2 ; evalf(%) ; # R. J. Mathar, Nov 14 2014

Mathematica

RealDigits[Total[1/GoldenRatio^{1, 3, 5, 7}], 10, 120][[1]] (* Harvey P. Dale, Apr 17 2023 *)

Crossrefs

Cf. A094214, A249600.

Sequence in context: A258942 A378967 A397009 * A298524 A212005 A199003

Adjacent sequences: A249598 A249599 A249600 * A249602 A249603 A249604

Keyword

nonn,cons

Author

N. J. A. Sloane, Nov 02 2014

Status

approved