A157259 - OEIS

A157259

Decimal expansion of 7 - 2*sqrt(2).

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

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OFFSET

1,1

COMMENTS

lim_{n -> infinity} b(n)/b(n-1) = (7+2*sqrt(2))/(7-2*sqrt(2)) for n mod 3 = {1, 2}, b = A129288.

lim_{n -> infinity} b(n)/b(n-1) = (7+2*sqrt(2))/(7-2*sqrt(2)) for n mod 3 = {0, 2}, b = A157257.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Pierre-Antoine Guihéneuf, Rotations Discrètes, Images des Mathématiques, CNRS, 2018. See 3-2*sqrt(2), the fractional part of this constant, about the loss of information when rotating an image.

Index entries for algebraic numbers, degree 2

FORMULA

Equals 3 + Sum_{k>=0} binomial(2*k,k)/((k+1) * 8^k). - Amiram Eldar, Aug 03 2020

Equals 4 + exp(-arccosh(3)). - Amiram Eldar, Jul 06 2023

Equals 4 + (2-sqrt(2))/(2+sqrt(2)). - Davide Rotondo, Jun 08 2024

EXAMPLE

7 - 2*sqrt(2) = 4.17157287525380990239...

MATHEMATICA

RealDigits[7-2*Sqrt[2], 10, 120][[1]] (* Harvey P. Dale, May 01 2012 *)

PROG

(PARI) 7 - 2*sqrt(2) \\ G. C. Greubel, Nov 28 2017

(Magma) [7 - 2*Sqrt(2)]; // G. C. Greubel, Nov 28 2017