A157349 Decimal expansion of (297 + 68*sqrt(2))/281.

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

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 (17 + 2*sqrt(2))/(17 - 2*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129626.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157348.

Minimal polynomial: 281*x^2 - 594*x + 281. - Amiram Eldar, May 05 2026

Example

1.39916911829669204027941221795821875210938678834744...

Mathematica

RealDigits[(297 + 68*Sqrt[2])/281, 10, 100][[1]] (* G. C. Greubel, Feb 01 2018 *)

Prog

(PARI) (297+68*sqrt(2))/281 \\ G. C. Greubel, Feb 01 2018
(Magma) (297+68*Sqrt(2))/281; // G. C. Greubel, Feb 01 2018

Crossrefs

Cf. A129626, A157348, A002193 (decimal expansion of sqrt(2)), A157350 (decimal expansion of (130803+73738*sqrt(2))/281^2).

Sequence in context: A103555 A388464 A360178 * A159811 A279134 A083352

Adjacent sequences: A157346 A157347 A157348 * A157350 A157351 A157352

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 12 2009

Status

approved