A160579 Decimal expansion of (204819+83570*sqrt(2))/409^2.

1, 9, 3, 0, 9, 1, 1, 6, 2, 4, 1, 9, 8, 3, 2, 2, 3, 0, 3, 3, 5, 9, 9, 5, 7, 9, 5, 5, 0, 7, 0, 8, 3, 5, 7, 1, 0, 1, 2, 8, 8, 6, 9, 8, 5, 7, 4, 5, 6, 9, 2, 3, 0, 8, 4, 3, 6, 3, 2, 8, 7, 6, 7, 5, 8, 5, 0, 1, 2, 9, 5, 0, 2, 0, 0, 6, 0, 7, 5, 3, 1, 7, 7, 9, 8, 9, 5, 4, 3, 7, 1, 6, 4, 8, 6, 6, 9, 0, 4, 3, 3, 0, 7, 1, 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 (610+137*sqrt(2))/(610-137*sqrt(2)).

Equals (3+2*sqrt(2))*(42-8*sqrt(2))^2/(42+8*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A129641.

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

Minimal polynomial: 167281*x^2 - 409638*x + 167281. - Amiram Eldar, Apr 28 2026

Example

1.93091162419832230335995795507083571012886985745692...

Mathematica

RealDigits[(204819+83570*Sqrt[2])/409^2, 10, 120][[1]] (* Harvey P. Dale, Jul 16 2013 *)

Prog

(PARI) (204819 +83570*sqrt(2))/409^2 \\ G. C. Greubel, Apr 08 2018
(Magma) (204819 +83570*Sqrt(2))/409^2; // G. C. Greubel, Apr 08 2018

Crossrefs

Cf. A129641, A160577, A002193 (decimal expansion of sqrt(2)), A160578 (decimal expansion of (473+168*sqrt(2))/409).

Sequence in context: A011461 A302716 A198546 * A134897 A010159 A097528

Adjacent sequences: A160576 A160577 A160578 * A160580 A160581 A160582

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 08 2009

Status

approved