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A060987 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. 2
1, 2, 3, 4, 7, 11, 18, 20, 31, 51, 69, 120, 189, 258, 327, 358, 427 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The correct sequence would be 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,... as computed by the Maple program. R. J. Mathar, Feb 25 2018

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..16.

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 A060986 for p values, A060988 for r values.

Sequence in context: A192669 A339484 A072164 * A006259 A119015 A222329

Adjacent sequences:  A060984 A060985 A060986 * A060988 A060989 A060990

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 11 2001

STATUS

approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)