The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A195550

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A195550

Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2.
(history; published version)

#10 by N. J. A. Sloane at Wed Dec 07 10:34:25 EST 2016

STATUS

editing

approved

#9 by N. J. A. Sloane at Wed Dec 07 10:34:23 EST 2016

KEYWORD

nonn,frac

STATUS

approved

editing

#8 by Michel Marcus at Sun Mar 09 13:40:14 EDT 2014

STATUS

proposed

approved

#7 by Jon E. Schoenfield at Sun Mar 09 13:20:24 EDT 2014

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sun Mar 09 13:20:21 EDT 2014

MATHEMATICA

(* by _Peter J. C. Moses, _, Sep 2 02 2011 *)

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:57:48 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Sep 21 2011

Discussion

Fri Mar 30

18:57

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

#4 by T. D. Noe at Wed Sep 21 16:44:58 EDT 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Wed Sep 21 16:17:34 EDT 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Wed Sep 21 14:49:41 EDT 2011

NAME

allocated for Clark KimberlingDenominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2.

DATA

3, 60, 660, 3597, 78480, 856080, 4669203, 101866380, 1111191780, 6060621597, 132222483360, 1442326073760, 7866682164003, 171624681534300, 1872138132549300, 10210947388253997, 222768704409038640, 2430033853722917040

OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

MATHEMATICA

r = 3/2; z = 21;

p[{f_, n_}] := (#1[[2]]/#1[[

1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

Array[FromContinuedFraction[

ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

{a, b} = ({Denominator[#1], Numerator[#1]} &)[

p[{r, z}]] (* A195550, A195551 *)

Sqrt[a^2 + b^2] (* A195552 *)

(* by Peter Moses, Sep 2 2011 *)

CROSSREFS

Cf. A195500, A195551, A195552.

KEYWORD

allocated

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Sep 21 2011

STATUS

approved

editing

#1 by Clark Kimberling at Tue Sep 20 09:47:36 EDT 2011

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved