A160578 Decimal expansion of (473+168*sqrt(2))/409.

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

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 (42+8*sqrt(2))/(42-8*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129641.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160577.

Minimal polynomial: 409*x^2 - 946*x + 409. - Amiram Eldar, Apr 28 2026

Example

1.73737867598699258728284524613014493202861827643845...

Mathematica

RealDigits[(473+168Sqrt[2])/409, 10, 120][[1]] (* Harvey P. Dale, Mar 05 2015 *)

Prog

(PARI) (473 +168*sqrt(2))/409 \\ G. C. Greubel, Apr 08 2018
(Magma) (473 +168*Sqrt(2))/409; // G. C. Greubel, Apr 08 2018

Crossrefs

Cf. A129641, A160577, A002193 (decimal expansion of sqrt(2)), A160579 (decimal expansion of (204819+83570*sqrt(2))/409^2).

Sequence in context: A242938 A085835 A153624 * A244258 A271178 A247950

Adjacent sequences: A160575 A160576 A160577 * A160579 A160580 A160581

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 08 2009

Status

approved