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Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives r values.
3

%I #5 Jan 12 2023 23:01:22

%S 1,1,2,2,4,6,10,11,17,28,38,66,104,142,180,197,377,574,612,1186,1383,

%T 2569,3952,5335,6718,8101,9484,10867,12250,12862,25112,35979,48841,

%U 73953,122794,171635,220476,256455,305296,525772,831068,1356840,2187908,3544748

%N Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives r values.

%H J. M. Barbour, <a href="http://www.jstor.org/stable/2304456">Music and Ternary Continued Fractions</a>, The American Mathematical Monthly, Vol. 55, No. 9 (Nov., 1948), pp. 545-555.

%H Viggo Brun, <a href="/A060986/a060986.pdf">Music and ternary continued fractions</a>, Kgl. Norske Videnskabers Selskab Forh., 23 (No. 10, 1950), pages 38-40. [Annotated scanned copy]

%H V. Brun, <a href="http://www.jstor.org/stable/24524581">Musikk og Euklidske algoritmer</a> (in Danish), Nordisk Mat. Tidskr, 9 (1961), 29-36.

%H J. B. Rosser, <a href="http://www.jstor.org/stable/2307936">Generalized Ternary Continued Fractions</a>, The American Mathematical Monthly, Vol. 57, No. 8 (Oct., 1950), pp. 528-535.

%p Digits := 100 :

%p c := evalf(log[10](5/4)) :

%p b := evalf(log[10](3/2)) :

%p a := evalf(log[10](2)) :

%p a3 := [1,0,0] :

%p b3 := [0,1,0] :

%p c3 := [0,0,1] :

%p for i from 1 to 30 do

%p a := a-b ;

%p b3 := [op(1,a3)+op(1,b3), op(2,a3)+op(2,b3), op(3,a3)+op(3,b3)] ;

%p if i > 2 then

%p printf("%d, ",b3[3]) ;

%p end if;

%p if a < b then

%p tmp := a ;

%p a := b;

%p b := tmp;

%p tmp3 := a3 ;

%p a3 := b3;

%p b3 := tmp3;

%p end if;

%p if b < c then

%p tmp3 := b ;

%p b := c;

%p c := tmp;

%p tmp3 := b3 ;

%p b3 := c3;

%p c3 := tmp3;

%p end if;

%p end do: # _R. J. Mathar_, Feb 25 2018

%Y See A359742 for p values, A359743 for q values.

%K nonn,easy

%O 0,3

%A _Sean A. Irvine_, Jan 12 2023