A159894 Decimal expansion of (731+54*sqrt(2))/727.

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

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 2.

Formula

Equals (27 +sqrt(2))/(27 -sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A130646.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A159893.

Minimal polynomial: 727*x^2 - 1462*x + 727. - Amiram Eldar, May 10 2026

Example

1.11054681206072507927825473329755666608357947905138...

Mathematica

RealDigits[(731+54Sqrt[2])/727, 10, 120][[1]] (* Harvey P. Dale, May 25 2013 *)

Prog

(PARI) (731 +54*sqrt(2))/727 \\ G. C. Greubel, May 17 2018
(Magma) (731 +54*Sqrt(2))/727; // G. C. Greubel, May 17 2018

Crossrefs

Cf. A130646, A159893, A002193 (decimal expansion of sqrt(2)), A159895 (decimal expansion of (1304787+843542*sqrt(2))/727^2).

Sequence in context: A190143 A089687 A251792 * A011502 A347185 A345231

Adjacent sequences: A159891 A159892 A159893 * A159895 A159896 A159897

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 30 2009

Status

approved