A187426 Decimal expansion of (3-phi)^2 = 10 - 5*phi where phi is the golden ratio.

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

Offset: 1

Author

Joost Gielen, Aug 30 2013

Keywords

• nonn
• cons

Comments

This is an integer in Q(sqrt(5)). - Wolfdieter Lang, Jan 07 2018

Examples

			1.909830...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A226765.

Apart from the first digit the same as A187798.

Programs

Mathematica

RealDigits[(3-GoldenRatio)^2,10,120][[1]] (* Harvey P. Dale, Jun 30 2017 *)

PARI

(15-5*sqrt(5))/2 \\ Charles R Greathouse IV, Aug 31 2013

PARI

polrootsreal(x^2-15*x+25)[1] \\ Charles R Greathouse IV, Feb 04 2025

Formula

(3-phi)^2 = 5/phi^2 = 10 - 5*phi.

Smaller root of x^2 - 15x + 25 = 0.

Equals 10*A187798-5. - R. J. Mathar, Feb 08 2023

Extensions

Corrected and extended by Charles R Greathouse IV, Aug 31 2013