A072223 Decimal expansion of unimodal analog of golden section with respect to A072176: a=lim A072176(n)/A072176(n+1).

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

Offset: 0

Author

Michele Dondi (bik.mido(AT)tiscalinet.it), Jul 04 2002

Keywords

• nonn
• easy
• cons

Comments

This is the smallest real root of (1-x^2)^2=x.

Examples

			0.52488859865640479389948613854...
		

Links

• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A072176, A072224.

Programs

Mathematica

RealDigits[ x /. FindRoot[ (1-x^2)^2==x, {x, 0.5}, WorkingPrecision->100 ], 10 ][ [ 1 ] ]

PARI

polrootsreal(x^4 - 2*x^2 - x + 1)[1] \\ Charles R Greathouse IV, Feb 11 2025