The On-Line Encyclopedia of Integer Sequences (OEIS)

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A081781

Continued cotangent for square root of 5.
(history; published version)

#9 by Russ Cox at Fri Mar 30 18:39:16 EDT 2012

AUTHOR

_Benoit Cloitre (benoit7848c(AT)orange.fr), _, Apr 10 2003

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/216

#8 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

KEYWORD

nonn,new

nonn

AUTHOR

Benoit Cloitre (abmtbenoit7848c(AT)wanadooorange.fr), Apr 10 2003

#7 by N. J. A. Sloane at Wed Dec 06 03:00:00 EST 2006

KEYWORD

nonn,cons,new

nonn

#6 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

sqrt(5)=cot(sum(n>=0, n, (-1)^n*acot(a(n))); let b(0)=sqrt(3), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n))

KEYWORD

nonn,cons,new

#5 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

KEYWORD

nonn,cons,new

AUTHOR

Benoit Cloitre (abcloitreabmt(AT)modulonetwanadoo.fr), Apr 10 2003

#4 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

KEYWORD

nonn,cons,new

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoomodulonet.fr), Apr 10 2003

#3 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

PROG

(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=sqrt(5); ?for(n=2, 10, bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1))

KEYWORD

nonn,cons,new

#2 by N. J. A. Sloane at Sat Sep 13 03:00:00 EDT 2003

FORMULA

sqrt(5)=cot(sum(n>=0,n,(-1)^n*acot(a(n))) ; let b(0)=sqrt(3), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n))

KEYWORD

nonn,cons,new

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Continued cotangent for square root of 5.

DATA

2, 23, 2961, 9798690, 110528843365255, 16850689692769666225948933906, 357017084742873887104901208145335336566095925224005385073, 137046393407742688281781643318644289249627231296779665713406441509975367310318242383523303176564909084594247359836

OFFSET

0,1

FORMULA

sqrt(5)=cot(sum(n>=0,n,(-1)^n*acot(a(n))) ; let b(0)=sqrt(3), b(n)=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)) then a(n)=floor(b(n))

PROG

(PARI) ?bn=vector(100); b(n)=if(n<0, 0, bn[n]); bn[1]=sqrt(5); ?for(n=2, 10, bn[n]=(b(n-1)*floor(b(n-1))+1)/(b(n-1)-floor(b(n-1)))) ?a(n)=floor(b(n+1))

CROSSREFS

Cf. A002666, A002667.

KEYWORD

nonn,cons

AUTHOR

Benoit Cloitre (abcloitre(AT)wanadoo.fr), Apr 10 2003

STATUS

approved