A385447 - OEIS

A385447

Decimal expansion of sqrt(8 + 9*phi), with the golden section A001622.

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

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OFFSET

1,1

COMMENTS

This constant c gives sqrt(11)*rho_1, where rho_1 = length(Z, D_1), with the fixed point Z = -(A385445 + A385446*i)/(2*11) of the complex map w given in A385445 and D_1 = i.

See A385445 for details and the linked paper, eq. (7b).

LINKS

Table of n, a(n) for n=1..84.

Index entries for algebraic numbers, degree 4.

FORMULA

Equals sqrt(8 + 9*phi) = sqrt(5 + 7*phi)*s, with s = A182007, the length of the side of a regular pentagon circumcribed by a unit circle.

EXAMPLE

4.7499795682454312672720369270371548927...

MATHEMATICA

RealDigits[Sqrt[8 + 9*GoldenRatio], 10, 120][[1]] (* Amiram Eldar, Jul 02 2025 *)

PROG

(PARI) sqrt(12.5+9*sqrt(5)/2) \\ Charles R Greathouse IV, May 18 2026