A157300 Decimal expansion of (1683 + 58*sqrt(2))/41^2.

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

Offset

1,3

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Equals (58+sqrt(2))/(58-sqrt(2)).

Equals (3+2*sqrt(2))*(7-2*sqrt(2))^2/(7+2*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A129288.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A157257.

Minimal polynomial: 1681*x^2 - 3366*x + 1681. - Amiram Eldar, May 07 2026

Example

1.049984763008708811915822692447449428052969047455004...

Maple

evalf((1683+58*sqrt(2))/41^2, 120); # Muniru A Asiru, Sep 28 2018

Mathematica

RealDigits[(1683+58Sqrt[2])/41^2, 10, 120][[1]] (* Harvey P. Dale, May 05 2014 *)

Prog

(PARI) default(realprecision, 100); (1683+58*sqrt(2))/41^2 \\ G. C. Greubel, Sep 28 2018
(Magma) SetDefaultRealField(RealField(100)); (1683+58*Sqrt(2))/41^2; // G. C. Greubel, Sep 28 2018

Crossrefs

Cf. A129288, A157257, A002193 (decimal expansion of sqrt(2)), A157260 (decimal expansion of (57+28*sqrt(2))/41).

Sequence in context: A200642 A209674 A364821 * A100555 A250126 A186887

Adjacent sequences: A157297 A157298 A157299 * A157301 A157302 A157303

Keyword

cons,nonn

Author

Klaus Brockhaus, May 01 2009

Status

approved