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 A330237 #18 Dec 21 2024 17:50:38 %S A330237 0,1,1,2,0,2,3,1,1,3,4,2,0,2,4,5,3,1,1,3,5,6,4,2,0,2,4,6,7,5,3,1,1,3, %T A330237 5,7,8,6,4,2,0,2,4,6,8,11,7,5,3,1,1,3,5,7,11,10,12,6,4,2,0,2,4,6,12, %U A330237 10,11,11,13,5,3,1,1,3,5,13,11,11,12,10,12,14,4,2,0,2,4,14,12,10,12,13,11,11,13,15,3,1,1,3,15,13,11,11,13,14,12,10,12,14,16,2,0,2,16 %N A330237 Square array T(n,k): concatenate the absolute differences of the digits of n and k (the smaller one padded with leading zeros); read by antidiagonals; n, k >= 1. %C A330237 A digit-wise analog of A049581. %C A330237 The binary operator T: N x N -> N is commutative, therefore this table is symmetric and it does not matter in which direction the antidiagonals are read. It would also be sufficient to specify only the lower half of the square table: see A330238 for this variant. The operator is also defined for either argument equal to 0, which is the neutral element: T(x,0) = 0 for all x. Therefore we omit row & column 0 here, see A330240 for the table including these. Every element is its opposite or inverse, as shown by the zero diagonal T(x,x) = 0. %H A330237 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2019/12/the-box-operation.html">The box ■ operation</a>, personal blog "Cinquante signes", and post to the SeqFan list, Dec 06 2019. %H A330237 Eric Angelini, <a href="/A330237/a330237.pdf">The box ■ operation</a>, personal blog "Cinquante signes", and post to the SeqFan list, Dec 06 2019. [Cached copy] %e A330237 The square array starts as follows: %e A330237 n | k=1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ... %e A330237 ---+----------------------------------------------------------- %e A330237 1 | 0 1 2 3 4 5 6 7 8 11 10 11 12 13 14 15 16 17 ... %e A330237 2 | 1 0 1 2 3 4 5 6 7 12 11 10 11 12 13 14 15 16 ... %e A330237 3 | 2 1 0 1 2 3 4 5 6 13 12 11 10 11 12 13 14 15 ... %e A330237 4 | 3 2 1 0 1 2 3 4 5 14 13 12 11 10 11 12 13 14 ... %e A330237 5 | 4 3 2 1 0 1 2 3 4 15 14 13 12 11 10 11 12 13 ... %e A330237 6 | 5 4 3 2 1 0 1 2 3 16 15 14 13 12 11 10 11 12 ... %e A330237 7 | 6 5 4 3 2 1 0 1 2 17 16 15 14 13 12 11 10 11 ... %e A330237 8 | 7 6 5 4 3 2 1 0 1 18 17 16 15 14 13 12 11 10 ... %e A330237 9 | 8 7 6 5 4 3 2 1 0 19 18 17 16 15 14 13 12 11 ... %e A330237 10 | 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 ... %e A330237 11 | 10 11 12 13 14 15 16 17 18 1 0 1 2 3 4 5 6 7 ... %e A330237 12 | 11 10 11 12 13 14 15 16 17 2 1 0 1 2 3 4 5 6 ... %e A330237 (...) %e A330237 It differs from A049581 only if at least one index is > 10. %o A330237 (PARI) T(a,b)=fromdigits(abs(Vec(digits(min(a,b)),-logint(a=max(a,b),10)-1)-digits(a))) %Y A330237 Cf A330240 (variant including row & column 0), A330237 (lower left triangle), A049581 (T(n,k) = |n-k|). %K A330237 nonn,base,tabl %O A330237 1,4 %A A330237 _M. F. Hasler_, Dec 06 2019