cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A348051 #7 Oct 07 2021 07:10:24
%S A348051 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,
%T A348051 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,
%U A348051 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
%N 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.
%C A348051 The velocities are assumed to be given in units of c, and thus c = 1.
%H A348051 Wikipedia, <a href="https://en.wikipedia.org/wiki/Velocity-addition_formula">Velocity-addition formula</a>.
%e A348051 The triangle of added fractions begins:
%e A348051      u   1/2   1/3   2/3   1/4   2/5   3/5   3/4   1/5   2/7   3/8   3/7
%e A348051    v \    .     .     .     .     .     .     .     .     .     .     .
%e A348051   1/2 |  4/5    .     .     .     .     .     .     .     .     .     .
%e A348051   1/3 |  5/7   3/5    .     .     .     .     .     .     .     .     .
%e A348051   2/3 |  7/8   9/11 12/13   .     .     .     .     .     .     .     .
%e A348051   1/4 |  2/3   7/13 11/14  8/17   .     .     .     .     .     .     .
%e A348051   2/5 |  3/4  11/17 16/19 13/22 20/29   .     .     .     .     .     .
%e A348051   3/5 | 11/13  7/9  19/21 17/23 25/31 15/17   .     .     .     .     .
%e A348051   3/4 | 10/11 13/15 17/18 16/19 23/26 27/29 24/25   .     .     .     .
%e A348051   1/5 |  7/11  1/2  13/17  3/7   5/9   5/7  19/23  5/13   .     .     .
%e A348051   2/7 | 11/16 13/23  4/5   1/2   8/13 31/41 29/34 17/37 28/53   .     .
%e A348051   3/8 | 14/19 17/27  5/6   4/7  31/46 39/49 36/41 23/43 37/62 48/73   .
%e A348051   3/7 | 13/17  2/3  23/27 19/31 29/41  9/11 33/37 11/19  7/11  9/13 21/29
%Y A348051 A348052 are the corresponding denominators.
%Y A348051 Cf. A007305, A007306, A348131, A348132.
%K A348051 nonn,frac,tabl
%O A348051 2,1
%A A348051 _Hugo Pfoertner_, Sep 25 2021