A159643 Decimal expansion of (1084467 + 707402*sqrt(2))/647^2.

4, 9, 8, 0, 5, 0, 5, 6, 8, 0, 5, 9, 8, 9, 6, 5, 1, 0, 5, 1, 7, 5, 5, 0, 3, 1, 7, 0, 9, 3, 8, 4, 8, 6, 3, 6, 8, 3, 6, 8, 4, 3, 6, 9, 5, 1, 8, 7, 0, 1, 3, 1, 3, 6, 5, 6, 9, 2, 8, 7, 7, 1, 2, 4, 0, 3, 2, 4, 9, 8, 4, 3, 3, 4, 5, 2, 3, 4, 2, 0, 2, 6, 8, 0, 0, 2, 8, 8, 1, 9, 8, 6, 7, 3, 3, 2, 5, 9, 5, 2, 9, 4, 3, 9, 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 (1226 + 577*sqrt(2))/(1226 - 577*sqrt(2)).

Equals (3 + 2*sqrt(2))*(36 - sqrt(2))^2/(36 + sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A130013.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159641.

Minimal polynomial: 418609*x^2 - 2168934*x + 418609. - Amiram Eldar, May 07 2026

Example

4.98050568059896510517550317093848636836843695187013...

Mathematica

RealDigits[(1084467+707402*Sqrt[2])/647^2, 10, 100][[1]] (* G. C. Greubel, May 10 2018 *)

Prog

(PARI) (1084467+707402*sqrt(2))/647^2 \\ G. C. Greubel, May 10 2018
(Magma) (1084467+707402*Sqrt(2))/647^2; // G. C. Greubel, May 10 2018

Crossrefs

Cf. A130013, A159641, A002193 (decimal expansion of sqrt(2)), A159642 (decimal expansion of (649+36*sqrt(2))/647).

Sequence in context: A096982 A212877 A205297 * A200398 A145424 A200394

Adjacent sequences: A159640 A159641 A159642 * A159644 A159645 A159646

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 21 2009

Status

approved