A359742 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 p values.

2, 3, 5, 7, 12, 19, 31, 34, 53, 87, 118, 205, 323, 441, 559, 612, 1171, 1783, 1901, 3684, 4296, 7980, 12276, 16572, 20868, 25164, 29460, 33756, 38052, 39953, 78005, 111761, 151714, 229719, 381433, 533147, 684861, 796622, 948336, 1633197, 2581533, 4214730

Offset

0,1

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..41.

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[1]) ;
    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 A359743 for q values, A359744 for r values.

Sequence in context: A192685 A293543 A060986 * A054540 A216231 A117537

Adjacent sequences: A359739 A359740 A359741 * A359743 A359744 A359745

Keyword

nonn,easy

Author

Sean A. Irvine, Jan 12 2023

Status

approved