A159567 Decimal expansion of (137283+87958*sqrt(2))/241^2.

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

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 (442+199*sqrt(2))/(442-199*sqrt(2)).

Equals (3+2*sqrt(2))*(22-sqrt(2))^2/(22+sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A129991.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159565.

Minimal polynomial: 58081*x^2 - 274566*x + 58081. - Amiram Eldar, May 05 2026

Example

4.50533559200448846098550191635881998579279280340224...

Mathematica

RealDigits[(137283+87958*Sqrt[2])/241^2, 10, 100][[1]] (* G. C. Greubel, May 05 2018 *)

Prog

(PARI) (137283+87958*sqrt(2))/241^2 \\ G. C. Greubel, May 05 2018
(Magma) (137283+87958*Sqrt(2))/241^2; // G. C. Greubel, May 05 2018

Crossrefs

Cf. A129991, A159565, A002193 (decimal expansion of sqrt(2)), A159566 (decimal expansion of (243+22*sqrt(2))/241).

Sequence in context: A391442 A187045 A186930 * A164357 A092487 A322505

Adjacent sequences: A159564 A159565 A159566 * A159568 A159569 A159570

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 16 2009

Status

approved