A359743 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 q values.

1, 2, 3, 4, 7, 11, 18, 20, 31, 51, 69, 120, 189, 258, 327, 358, 685, 1043, 1112, 2155, 2513, 4668, 7181, 9694, 12207, 14720, 17233, 19746, 22259, 23371, 45630, 65376, 88747, 134377, 223124, 311871, 400618, 465994, 554741, 955359, 1510100, 2465459, 3975559

Offset

0,2

References

V. Brun, Music and ternary continued fractions, Kgl. Norske Videnskabers Selskab Forh., 23 (No. 10, 1950).

Links

Table of n, a(n) for n=0..42.

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[2]) ;
    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, A359744 for r values.

Sequence in context: A339484 A072164 A060987 * A006259 A119015 A222329

Adjacent sequences: A359740 A359741 A359742 * A359744 A359745 A359746

Keyword

nonn,easy

Author

Sean A. Irvine, Jan 12 2023

Status

approved