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A348051
Triangle T(j,k) of numerators of relativistically added fractional velocities w(u,v)=(u+v)/(u*v+1), with velocities enumerated by the Farey series, i.e., u(m) = v(m) = A007305(m)/A007306(m), m>=2.
3
4, 5, 3, 7, 9, 12, 2, 7, 11, 8, 3, 11, 16, 13, 20, 11, 7, 19, 17, 25, 15, 10, 13, 17, 16, 23, 27, 24, 7, 1, 13, 3, 5, 5, 19, 5, 11, 13, 4, 1, 8, 31, 29, 17, 28, 14, 17, 5, 4, 31, 39, 36, 23, 37, 48, 13, 2, 23, 19, 29, 9, 33, 11, 7, 9, 21, 5, 19, 26, 23, 34, 41, 37, 9, 14, 53, 49, 56
OFFSET
2,1
COMMENTS
The velocities are assumed to be given in units of c, and thus c = 1.
EXAMPLE
The triangle of added fractions begins:
u 1/2 1/3 2/3 1/4 2/5 3/5 3/4 1/5 2/7 3/8 3/7
v \ . . . . . . . . . . .
1/2 | 4/5 . . . . . . . . . .
1/3 | 5/7 3/5 . . . . . . . . .
2/3 | 7/8 9/11 12/13 . . . . . . . .
1/4 | 2/3 7/13 11/14 8/17 . . . . . . .
2/5 | 3/4 11/17 16/19 13/22 20/29 . . . . . .
3/5 | 11/13 7/9 19/21 17/23 25/31 15/17 . . . . .
3/4 | 10/11 13/15 17/18 16/19 23/26 27/29 24/25 . . . .
1/5 | 7/11 1/2 13/17 3/7 5/9 5/7 19/23 5/13 . . .
2/7 | 11/16 13/23 4/5 1/2 8/13 31/41 29/34 17/37 28/53 . .
3/8 | 14/19 17/27 5/6 4/7 31/46 39/49 36/41 23/43 37/62 48/73 .
3/7 | 13/17 2/3 23/27 19/31 29/41 9/11 33/37 11/19 7/11 9/13 21/29
CROSSREFS
A348052 are the corresponding denominators.
Sequence in context: A268741 A263031 A004493 * A328238 A170929 A245085
KEYWORD
nonn,frac,tabl
AUTHOR
Hugo Pfoertner, Sep 25 2021
STATUS
approved