A160056 Decimal expansion of (107+42*sqrt(2))/89.

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

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 (14+3*sqrt(2))/(14-3*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129298.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160055.

Minimal polynomial: 89*x^2 - 214*x + 89. - Amiram Eldar, May 11 2026

Example

1.86962887213112350617607782490794740786433953669473...

Mathematica

RealDigits[(107+42*Sqrt[2])/89, 10, 100][[1]] (* G. C. Greubel, Apr 15 2018 *)

Prog

(PARI) (107+42*sqrt(2))/89 \\ G. C. Greubel, Apr 15 2018
(Magma) (107+42*Sqrt(2))/89; // G. C. Greubel, Apr 15 2018

Crossrefs

Cf. A129298, A160055, A002193 (decimal expansion of sqrt(2)), A160057 (decimal expansion of (8979+2990*sqrt(2))/89^2).

Sequence in context: A021096 A021119 A256686 * A155680 A249103 A382005

Adjacent sequences: A160053 A160054 A160055 * A160057 A160058 A160059

Keyword

cons,nonn

Author

Klaus Brockhaus, May 04 2009

Status

approved