OFFSET
1,1
COMMENTS
The sequence are the terms in a triangle, where the rows correspond to the denominator of the rational number (starting with row 2, column 1) and the columns correspond to the numerators:
x = 1 2 3 4 5 Rationals x/y:
Row 1: (y=2) 6 1/2
Row 2: (y=3) 15, 5 1/3, 2/3
Row 3: (y=4) 22, 6, 3 1/4, 2/4, 3/4
Row 4: (y=5) 30, 9, 7, 2 1/5, 2/5, 3/5, 4/5
Row 5: (y=6) 45, 15, 6, 5, 1 1/6, 2/6, 3/6, 4/6, 5/6
LINKS
Jud McCranie, Table of n, a(n) for n = 1..990
EXAMPLE
The sixth rational number is 3/4;
3/4 = 1/2 + 1/5 + 1/20
= 1/2 + 1/6 + 1/12
= 1/3 + 1/4 + 1/5,
so a(6)=3.
PROG
(PARI) Efrac3(x, y)=sum(p=if(y%x, y\x, y\x+1), 3*y\x, my(N=x/y-1/p); sum(q=max(if(numerator(N)==1, 1\N+1, 1\N), p+1), 2\N, my(M=N-1/q, r=1/M); type(r)=="t_INT" && q<r))
row(n)=vector(n-1, x, Efrac3(x, n)) \\ Charles R Greathouse IV, Nov 09 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jud McCranie, Nov 09 2021
STATUS
approved