A157647 Decimal expansion of (33+8*sqrt(2))/31.

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

Offset: 1

Author

Klaus Brockhaus, Mar 11 2009

Keywords

• cons
• nonn

Comments

lim_{n -> infinity} b(n)/b(n-1) = (33+8*sqrt(2))/31 for n mod 3 = {1, 2}, b = A118674.

lim_{n -> infinity} b(n)/b(n-1) = (33+8*sqrt(2))/31 for n mod 3 = {0, 2}, b = A157646.

Examples

			(33+8*sqrt(2))/31 = 1.42947446770918581904...
		

Links

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

Crossrefs

A118674, A157646, A002193 (decimal expansion of sqrt(2)), A157648 (decimal expansion of (1539+850*sqrt(2))/31^2).

Programs

Magma

(33+8*Sqrt(2))/31; // G. C. Greubel, Mar 30 2018

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((33+8*sqrt(2))/31))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(33+8*Sqrt[2])/31,10,120][[1]] (* Harvey P. Dale, Mar 02 2014 *)

PARI

(33+8*sqrt(2))/31 \\ G. C. Greubel, Mar 30 2018

Formula

(33+8*sqrt(2))/31 = (8+sqrt(2))/(8-sqrt(2)).