A161480 Decimal expansion of (129 + 44*sqrt(2))/113.

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

Offset

1,2

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Equals (11 + 2*sqrt(2))/(11 - 2*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A161478.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A161479.

Minimal polynomial: 113*x^2 - 258*x + 113. - Amiram Eldar, May 02 2026

Example

1.69226014818067417829446286606395323413332356209367...

Maple

with(MmaTranslator[Mma]): Digits:=150:
RealDigits(evalf((129+44*sqrt(2))/113))[1]; # Muniru A Asiru, Apr 08 2018

Mathematica

RealDigits[(129 +44*Sqrt[2])/113, 10, 100][[1]] (* G. C. Greubel, Apr 07 2018 *)

Prog

(PARI) (129 +44*sqrt(2))/113 \\ G. C. Greubel, Apr 07 2018
(Magma) (129 +44*Sqrt(2))/113; // G. C. Greubel, Apr 07 2018

Crossrefs

Cf. A161478, A161479, A002193 (decimal expansion of sqrt(2)), A161481 (decimal expansion of (16131+6970*sqrt(2))/113^2).

Sequence in context: A197696 A072364 A087016 * A309819 A309825 A289503

Adjacent sequences: A161477 A161478 A161479 * A161481 A161482 A161483

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 13 2009

Status

approved