The On-Line Encyclopedia of Integer Sequences (OEIS)

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A159779

Decimal expansion of (56211+34510*sqrt(2))/167^2.
(history; published version)

#10 by Charles R Greathouse IV at Thu Sep 08 08:45:44 EDT 2022

PROG

(MAGMAMagma) (56211 +34510*Sqrt(2))/167^2 // G. C. Greubel, May 21 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#9 by Susanna Cuyler at Tue May 22 05:43:47 EDT 2018

STATUS

proposed

approved

#8 by Michel Marcus at Tue May 22 02:36:33 EDT 2018

STATUS

editing

proposed

#7 by Michel Marcus at Tue May 22 02:36:29 EDT 2018

COMMENTS

Equals Lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 0, b = A130608.

Equals Lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 1, b = A159777.

STATUS

proposed

editing

#6 by Jon E. Schoenfield at Tue May 22 00:46:51 EDT 2018

STATUS

editing

proposed

#5 by Jon E. Schoenfield at Tue May 22 00:46:48 EDT 2018

COMMENTS

lim_Lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 0, b = A130608.

lim_Lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 1, b = A159777.

FORMULA

Equals (290 + 119*sqrt(2))/(290 - 119*sqrt(2)).

Equals (3 + 2*sqrt(2))*(13 - sqrt(2))^2/(13 + sqrt(2))^2.

STATUS

proposed

editing

#4 by G. C. Greubel at Mon May 21 23:32:14 EDT 2018

STATUS

editing

proposed

#3 by G. C. Greubel at Mon May 21 23:31:49 EDT 2018

LINKS

G. C. Greubel, <a href="/A159779/b159779.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

(56211+34510*sqrt(2))/167^2 = Equals (290 +119*sqrt(2))/(290 -119*sqrt(2)).

= Equals (3 +2*sqrt(2))*(13 -sqrt(2))^2/(13 +sqrt(2))^2.

MATHEMATICA

RealDigits[(56211 +34510*Sqrt[2])/167^2, 10, 100][[1]] (* G. C. Greubel, May 21 2018 *)

PROG

(PARI) (56211 +34510*sqrt(2))/167^2 \\ G. C. Greubel, May 21 2018

(MAGMA) (56211 +34510*Sqrt(2))/167^2 // G. C. Greubel, May 21 2018

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:28:01 EDT 2012

AUTHOR

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Apr 30 2009

Discussion

Fri Mar 30

17:28

OEIS Server: https://oeis.org/edit/global/145

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Decimal expansion of (56211+34510*sqrt(2))/167^2.

DATA

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

OFFSET

1,1

COMMENTS

lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 0, b = A130608.

lim_{n -> infinity} b(n)/b(n-1) = (56211+34510*sqrt(2))/167^2 for n mod 3 = 1, b = A159777.

FORMULA

(56211+34510*sqrt(2))/167^2 = (290+119*sqrt(2))/(290-119*sqrt(2))

= (3+2*sqrt(2))*(13-sqrt(2))^2/(13+sqrt(2))^2.

EXAMPLE

(56211+34510*sqrt(2))/167^2 = 3.76548137392862813776...

CROSSREFS

Cf. A130608, A159777, A002193 (decimal expansion of sqrt(2)), A159778 (decimal expansion of (171+26*sqrt(2))/167).

KEYWORD

cons,nonn

AUTHOR

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2009

STATUS

approved