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.
%I A157806 #7 Feb 03 2021 21:41:46
%S A157806 0,1,1,2,2,3,1,1,3,4,4,5,3,1,1,3,5,6,2,2,6,7,5,1,1,5,7,8,4,4,8,9,7,5,
%T A157806 3,1,1,3,5,7,9,10,2,2,10,11,9,7,5,3,1,1,3,5,7,9,11,12,8,4,4,8,12,13,
%U A157806 11,7,1,1,7,11,13,14,10,6,2,2,6,10,14,15,13,11
%N A157806 Absolute value of the difference between numerator and denominator of fractions arranged by Cantor's ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, ...) with equivalent fractions removed.
%H A157806 Andrew Howroyd, <a href="/A157806/b157806.txt">Table of n, a(n) for n = 0..10000</a>
%o A157806 (PARI) seq(n)={my(L=List(), r=1, k=1); while(#L<=n, if(k==r, r++; k=0); k++; if(gcd(k,r-k)==1, listput(L, abs(r-2*k)))); Vec(L)} \\ _Andrew Howroyd_, Feb 03 2021
%Y A157806 Sum of numerator and denominator is given by A038567.
%K A157806 nonn,look
%O A157806 0,4
%A A157806 _Ron R. King_, Mar 07 2009
%E A157806 Terms a(56) and beyond from _Andrew Howroyd_, Feb 03 2021