A157648 Decimal expansion of (1539+850*sqrt(2))/31^2.

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

Offset: 1

Author

Klaus Brockhaus, Mar 11 2009

Keywords

• cons
• nonn
• easy

Comments

Limit_{n -> oo} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 0, b = A118674.

Limit_{n -> oo} b(n)/b(n-1) = (1539+850*sqrt(2))/31^2 for n mod 3 = 1, b = A157646.

Examples

			2.85232208950794046980...
		

Links

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

Crossrefs

Cf. A118674, A157646, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157647 (decimal expansion of (33+8*sqrt(2))/31).

Programs

Magma

(1539+850*Sqrt(2))/31^2; // G. C. Greubel, Mar 30 2018

Maple

with(MmaTranslator[Mma]): Digits:=100:
RealDigits(evalf((1539+850*sqrt(2))/31^2))[1]; # Muniru A Asiru, Mar 31 2018

Mathematica

RealDigits[(1539+850*Sqrt[2])/31^2, 10, 100][[1]] (* G. C. Greubel, Mar 30 2018 *)

PARI

(1539+850*sqrt(2))/31^2 \\ G. C. Greubel, Mar 30 2018

Formula

Equals (50+17*sqrt(2))/(50-17*sqrt(2)).

Equals (3+2*sqrt(2))*(8-sqrt(2))^2/(8+sqrt(2))^2.