A160178 Decimal expansion of (755667+461578*sqrt(2))/617^2.

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

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 2.

Formula

Equals (1066 + 433*sqrt(2))/(1066 - 433*sqrt(2)).

Equals (3 + 2*sqrt(2))*(25 - 2*sqrt(2))^2/(25 + 2*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A115135.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A160176.

Minimal polynomial: 380689*x^2 - 1511334*x + 380689. - Amiram Eldar, May 11 2026

Example

3.69970466100425404053121019504967051769300401349327...

Mathematica

RealDigits[(755667+461578*Sqrt[2])/617^2, 10, 120][[1]] (* Harvey P. Dale, Oct 14 2017 *)

Prog

(PARI) (755667+461578*sqrt(2))/617^2 \\ G. C. Greubel, Apr 25 2018
(Magma) (755667+461578*Sqrt(2))/617^2; // G. C. Greubel, Apr 25 2018

Crossrefs

Cf. A115135, A160176, A002193 (decimal expansion of sqrt(2)), A160177 (decimal expansion of (633+100*sqrt(2))/617).

Sequence in context: A397204 A198373 A331065 * A011383 A329513 A329213

Adjacent sequences: A160175 A160176 A160177 * A160179 A160180 A160181

Keyword

cons,nonn

Author

Klaus Brockhaus, May 18 2009

Status

approved