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.

1, 1, 2, 2, 4, 6, 10, 11, 17, 28, 38, 66, 104, 142, 180, 197, 377, 574, 612, 1186, 1383, 2569, 3952, 5335, 6718, 8101, 9484, 10867, 12250, 12862, 25112, 35979, 48841, 73953, 122794, 171635, 220476, 256455, 305296, 525772, 831068, 1356840, 2187908, 3544748

Offset

0,3

Links

Table of n, a(n) for n=0..43.

J. M. Barbour, Music and Ternary Continued Fractions, The American Mathematical Monthly, Vol. 55, No. 9 (Nov., 1948), pp. 545-555.

Viggo Brun, Music and ternary continued fractions, Kgl. Norske Videnskabers Selskab Forh., 23 (No. 10, 1950), pages 38-40. [Annotated scanned copy]

V. Brun, Musikk og Euklidske algoritmer (in Danish), Nordisk Mat. Tidskr, 9 (1961), 29-36.

J. B. Rosser, Generalized Ternary Continued Fractions, The American Mathematical Monthly, Vol. 57, No. 8 (Oct., 1950), pp. 528-535.

Maple

Digits := 100 :
c := evalf(log[10](5/4)) :
b := evalf(log[10](3/2)) :
a := evalf(log[10](2)) :
a3 := [1, 0, 0] :
b3 := [0, 1, 0] :
c3 := [0, 0, 1] :
for i from 1 to 30 do
    a := a-b ;
    b3 := [op(1, a3)+op(1, b3), op(2, a3)+op(2, b3), op(3, a3)+op(3, b3)] ;
    if i > 2 then
        printf("%d, ", b3[3]) ;
    end if;
    if a < b then
        tmp := a ;
        a := b;
        b := tmp;
        tmp3 := a3 ;
        a3 := b3;
        b3 := tmp3;
    end if;
    if b < c then
        tmp3 := b ;
        b := c;
        c := tmp;
        tmp3 := b3 ;
        b3 := c3;
        c3 := tmp3;
    end if;
end do: # R. J. Mathar, Feb 25 2018

Crossrefs

See A359742 for p values, A359743 for q values.

Sequence in context: A308907 A285908 A060988 * A308956 A309834 A326448

Adjacent sequences: A359741 A359742 A359743 * A359745 A359746 A359747

Keyword

nonn,easy

Author

Sean A. Irvine, Jan 12 2023

Status

approved