A159846 Decimal expansion of (293619 + 186550*sqrt(2))/359^2.

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

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 (650 + 287*sqrt(2))/(650 - 287*sqrt(2)).

Equals (3 + 2*sqrt(2))*(19 - sqrt(2))^2/(19 + sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A130610.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159844.

Minimal polynomial: 128881*x^2 - 587238*x + 128881. - Amiram Eldar, May 10 2026

Example

4.32523444154453240860914356267657122894121156998758...

Mathematica

RealDigits[(293619+186550Sqrt[2])/359^2, 10, 120][[1]] (* Harvey P. Dale, Jun 14 2011 *)

Prog

(PARI) (293619 +186550*sqrt(2))/359^2 \\ _G. C Greubel_, May 19 2018
(Magma) (293619 +186550*Sqrt(2))/359^2; // G. C. Greubel, May 19 2018

Crossrefs

Cf. A130610, A159844, A002193 (decimal expansion of sqrt(2)), A159845 (decimal expansion of (363+38*sqrt(2))/359).

Sequence in context: A244951 A110631 A333669 * A377512 A384440 A071890

Adjacent sequences: A159843 A159844 A159845 * A159847 A159848 A159849

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 30 2009

Status

approved