A160201 Decimal expansion of (1003+462*sqrt(2))/761.

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

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 (42 + 11*sqrt(2))/(42 - 11*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A122694.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160200.

Minimal polynomial: 761*x^2 - 2006*x + 761. - Amiram Eldar, May 11 2026

Example

2.17656592091507215840523021101823983219341446310663...

Mathematica

RealDigits[(1003+462*Sqrt[2])/761, 10, 120][[1]] (* Harvey P. Dale, Feb 07 2016 *)

Prog

(PARI) (1003+462*sqrt(2))/761 \\ G. C. Greubel, Apr 25 2018
(Magma) (1003+462*Sqrt(2))/761; // G. C. Greubel, Apr 25 2018

Crossrefs

Cf. A122694, A160200, A002193 (decimal expansion of sqrt(2)), A160202 (decimal expansion of (591603+85478*sqrt(2))/761^2).

Sequence in context: A329058 A078301 A391146 * A204912 A178049 A257577

Adjacent sequences: A160198 A160199 A160200 * A160202 A160203 A160204

Keyword

cons,nonn

Author

Klaus Brockhaus, May 18 2009

Status

approved