A159759 Decimal expansion of (83+18*sqrt(2))/79.

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

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A118676.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A159758.

Minimal polynomial: 79*x^2 - 166*x + 79. - Amiram Eldar, May 09 2026

Example

1.37285878636349001111937211437689323309182397160487...

Mathematica

RealDigits[(83+18Sqrt[2])/79, 10, 120][[1]] (* Harvey P. Dale, Jul 27 2017 *)

Prog

(PARI) (18*sqrt(2)+83)/79 \\ Charles R Greathouse IV, Jan 30 2018
(Magma) (83 +18*Sqrt(2))/79; // G. C. Greubel, May 22 2018

Crossrefs

Cf. A118676, A159758, A002193 (decimal expansion of sqrt(2)), A159760 (decimal expansion of (10659+6110*sqrt(2))/79^2).

Sequence in context: A363940 A199401 A261573 * A243964 A397550 A197837

Adjacent sequences: A159756 A159757 A159758 * A159760 A159761 A159762

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 30 2009

Status

approved