A157647 Decimal expansion of (33+8*sqrt(2))/31.

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

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 (8+sqrt(2))/(8-sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A118674.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157646.

Minimal polynomial: 31*x^2 - 66*x + 31. - Amiram Eldar, May 07 2026

Example

1.42947446770918581904559709011863176221152822590372...

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((33+8*sqrt(2))/31))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(33+8*Sqrt[2])/31, 10, 120][[1]] (* Harvey P. Dale, Mar 02 2014 *)

Prog

(PARI) (33+8*sqrt(2))/31 \\ G. C. Greubel, Mar 30 2018
(Magma) (33+8*Sqrt(2))/31; // G. C. Greubel, Mar 30 2018

Crossrefs

Cf. A118674, A157646, A002193 (decimal expansion of sqrt(2)), A157648 (decimal expansion of (1539+850*sqrt(2))/31^2).

Sequence in context: A051494 A262025 A118013 * A194108 A091452 A194032

Adjacent sequences: A157644 A157645 A157646 * A157648 A157649 A157650

Keyword

cons,nonn

Author

Klaus Brockhaus, Mar 11 2009

Status

approved