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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.
3
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
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
KEYWORD
nonn,easy
AUTHOR
Sean A. Irvine, Jan 12 2023
STATUS
approved