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