The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A190290

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A190290

Decimal expansion of (3+sqrt(21))/3.
(history; published version)

#8 by Joerg Arndt at Mon Aug 03 02:33:26 EDT 2020

STATUS

reviewed

approved

#7 by Michel Marcus at Mon Aug 03 02:07:23 EDT 2020

STATUS

proposed

reviewed

#6 by Amiram Eldar at Mon Aug 03 01:54:05 EDT 2020

STATUS

editing

proposed

#5 by Amiram Eldar at Mon Aug 03 01:47:29 EDT 2020

FORMULA

Equals 1 + Sum_{k>=0} binomial(2*k,k)/7^k. - Amiram Eldar, Aug 03 2020

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:57:27 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, May 07 2011

Discussion

Fri Mar 30

18:57

OEIS Server: https://oeis.org/edit/global/285

#3 by T. D. Noe at Sun May 08 16:23:18 EDT 2011

STATUS

proposed

approved

#2 by Clark Kimberling at Sat May 07 14:01:34 EDT 2011

NAME

allocated for Clark Kimberling

Decimal expansion of (3+sqrt(21))/3.

DATA

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

OFFSET

1,1

COMMENTS

The rectangle R whose shape (i.e., length/width) is (3+sqrt(21))/3, can be partitioned into rectangles of shapes 3/2 and 2 in a manner that matches the periodic continued fraction [2, 3/2, 2, 3/2, ...]. R can also be partitioned into squares so as to match the periodic continued fraction [2,1,1,8,1,1,2,1,1,8,1,1,2,,...]. For details, see A188635.

EXAMPLE

2.527525231651946668862682397909336162995...

MATHEMATICA

FromContinuedFraction[{2, 3/2, {2, 3/2}}]

ContinuedFraction[%, 100] (* [2, 1, 1, 8, 1, 1, 2, ... *)

RealDigits[N[%%, 120]] (* A190290 *)

N[%%%, 40]

CROSSREFS

Cf. A188635, A190289.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), May 07 2011

STATUS

approved

proposed

#1 by Clark Kimberling at Sat May 07 11:31:13 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved