A249600 Decimal expansion of 1/phi + 1/phi^3 + 1/phi^5, where phi is the golden ratio.

9, 4, 4, 2, 7, 1, 9, 0, 9, 9, 9, 9, 1, 5, 8, 7, 8, 5, 6, 3, 6, 6, 9, 4, 6, 7, 4, 9, 2, 5, 1, 0, 4, 9, 4, 1, 7, 6, 2, 4, 7, 3, 4, 3, 8, 4, 4, 6, 1, 0, 2, 8, 9, 7, 0, 8, 3, 5, 8, 8, 9, 8, 1, 6, 4, 2, 0, 8, 3, 7, 0, 2, 5, 5, 1, 2, 1, 9, 5, 9, 7, 6, 5, 7, 6, 5, 7, 6, 3, 3, 5, 1, 5, 1, 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..94.

Formula

Equals A010532 minus 8. - R. J. Mathar, Nov 09 2014

From Amiram Eldar, Dec 18 2025: (Start)

Minimal polynomial: x^2 + 16*x - 16.

Equals 4*(sqrt(5)-2).

Equals 8*phi - 12.

Equals 4/phi^3.

Equals Sum_{n>=1} (-1)^(n+1)/A156085(n). (End)

Equals 1 - 1/phi^6. - Peter Bala, Dec 30 2025

Example

0.944271909999158785636694674925104941762473438446102...

Mathematica

With[{g=GoldenRatio}, RealDigits[1/g+1/g^3+1/g^5, 10, 120][[1]]] (* Harvey P. Dale, Jul 16 2017 *)

Crossrefs

Cf. A001622, A010532, A094214, A156085, A249601.

Sequence in context: A382573 A389029 A388955 * A375274 A378331 A262313

Adjacent sequences: A249597 A249598 A249599 * A249601 A249602 A249603

Keyword

nonn,cons,easy

Author

N. J. A. Sloane, Nov 02 2014

Status

approved