# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a359744
Showing 1-1 of 1

%I A359744 #5 Jan 12 2023 23:01:22
%S A359744 1,1,2,2,4,6,10,11,17,28,38,66,104,142,180,197,377,574,612,1186,1383,
%T A359744 2569,3952,5335,6718,8101,9484,10867,12250,12862,25112,35979,48841,
%U A359744 73953,122794,171635,220476,256455,305296,525772,831068,1356840,2187908,3544748
%N A359744 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 A359744 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 A359744 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 A359744 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 A359744 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 A359744 Digits := 100 :
%p A359744 c := evalf(log[10](5/4)) :
%p A359744 b := evalf(log[10](3/2)) :
%p A359744 a := evalf(log[10](2)) :
%p A359744 a3 := [1,0,0] :
%p A359744 b3 := [0,1,0] :
%p A359744 c3 := [0,0,1] :
%p A359744 for i from 1 to 30 do
%p A359744     a := a-b ;
%p A359744     b3 := [op(1,a3)+op(1,b3), op(2,a3)+op(2,b3), op(3,a3)+op(3,b3)] ;
%p A359744     if i > 2 then
%p A359744         printf("%d, ",b3[3]) ;
%p A359744     end if;
%p A359744     if a < b then
%p A359744         tmp := a ;
%p A359744         a := b;
%p A359744         b := tmp;
%p A359744         tmp3 := a3 ;
%p A359744         a3 := b3;
%p A359744         b3 := tmp3;
%p A359744     end if;
%p A359744     if b < c then
%p A359744         tmp3 := b ;
%p A359744         b := c;
%p A359744         c := tmp;
%p A359744         tmp3 := b3 ;
%p A359744         b3 := c3;
%p A359744         c3 := tmp3;
%p A359744     end if;
%p A359744 end do: # _R. J. Mathar_, Feb 25 2018
%Y A359744 See A359742 for p values, A359743 for q values.
%K A359744 nonn,easy
%O A359744 0,3
%A A359744 _Sean A. Irvine_, Jan 12 2023

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE