A358664 Decimal expansion of ((phi + 1)^phi - 1) / phi, where phi is the golden ratio.

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

Offset

1,1

Links

Table of n, a(n) for n=1..93.

Formula

Equals (1 - (phi + 1)^(phi^2 - 1) / (1 - (phi + 1)), which is of the form (1 - a^(ab)) / (1 - a), where a = phi + 1 and b = phi - 1 (cf. A358661, A358662, and A358663 for constants related to this form).

Example

2.314955928829738451601640...

Mathematica

RealDigits[((GoldenRatio + 1)^GoldenRatio - 1)/GoldenRatio, 10,
  100][[1]]

Crossrefs

Cf. A001622 (phi), A358661, A358662, and A358663.

Sequence in context: A226392 A121340 A332635 * A231206 A165241 A119865

Adjacent sequences: A358661 A358662 A358663 * A358665 A358666 A358667

Keyword

nonn,cons

Author

Wesley Ivan Hurt, Nov 25 2022

Status

approved