A157471 Decimal expansion of (19491+12070*sqrt(2))/97^2.

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

Offset

1,1

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Equals (170+71*sqrt(2))/(170-71*sqrt(2)).

Equals (3+2*sqrt(2))*(14-sqrt(2))^2/(14+sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A129836.

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

Minimal polynomial: 9409*x^2 - 38982*x + 9409. - Amiram Eldar, May 04 2026

Example

3.88570067997058744170861758967064043026208306257835...

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((19491+12070*sqrt(2))/97^2))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(19491+12070*Sqrt[2])/97^2, 10, 100][[1]] (* G. C. Greubel, Mar 30 2018 *)

Prog

(PARI) (19491+12070*sqrt(2))/97^2 \\ G. C. Greubel, Mar 30 2018
(Magma) (19491+12070*Sqrt(2))/97^2; // G. C. Greubel, Mar 30 2018

Crossrefs

Cf. A129836, A157469, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157470 (decimal expansion of (99+14*sqrt(2))/97).

Sequence in context: A386736 A179553 A384287 * A288094 A131596 A384588

Adjacent sequences: A157468 A157469 A157470 * A157472 A157473 A157474

Keyword

cons,nonn

Author

Klaus Brockhaus, Mar 12 2009

Status

approved