A157470 Decimal expansion of (99+14*sqrt(2))/97.

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

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 (14+sqrt(2))/(14-sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129836.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157469.

Minimal polynomial: 97*x^2 - 198*x + 97. - Amiram Eldar, May 04 2026

Example

1.22473185436312712044560455813335848556675676551832...

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((99+14*sqrt(2))/97))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(99+14*Sqrt[2])/97, 10, 100][[1]] (* G. C. Greubel, Mar 30 2018 *)

Prog

(PARI) (99+14*sqrt(2))/97 \\ G. C. Greubel, Mar 30 2018
(Magma) (99+14*Sqrt(2))/97; // G. C. Greubel, Mar 30 2018

Crossrefs

Cf. A129836, A157469, A002193 (decimal expansion of sqrt(2)), A157471 (decimal expansion of (19491+12070*sqrt(2))/97^2).

Sequence in context: A354702 A350764 A249758 * A120280 A212362 A209142

Adjacent sequences: A157467 A157468 A157469 * A157471 A157472 A157473

Keyword

cons,nonn,easy

Author

Klaus Brockhaus, Mar 12 2009

Status

approved