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 A357144 #8 Sep 18 2022 12:37:49 %S A357144 0,0,0,0,1,0,0,2,2,0,0,3,8,3,0,0,4,1,1,4,0,0,5,32,15,32,5,0,0,6,14,6, %T A357144 6,14,6,0,0,7,4,7,256,7,4,7,0,0,8,5,9,2,2,9,5,8,0,0,9,128,63,48,35,48, %U A357144 63,128,9,0,0,10,6,2,1,1,1,1,2,6,10,0,0,11,56,27,2048,47,60,47,2048,27,56,11,0 %N A357144 Square array, A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = g(f(n) * f(k)) where f(m) = A002487(m)/A002487(m+1) and g is the inverse of f. %C A357144 The function f is a bijection from the nonnegative integers to the nonnegative rational numbers. %C A357144 The positive integers, together with (x,y) -> A(x,y), form an abelian group isomorph to the multiplicative group of positive rational numbers (f and g act as isomorphisms). %C A357144 Each row (or column), except the first, is a permutation of the nonnegative integers. %H A357144 Rémy Sigrist, <a href="/A357144/a357144.gp.txt">PARI program</a> %F A357144 A(n, k) = A(k, n). %F A357144 A(n, 0) = 0. %F A357144 A(n, 1) = n. %F A357144 A(n, A054429(n)) = 1 for any n > 0. %F A357144 A(m, A(n, k)) = A(A(m, n), k). %F A357144 A(n, A(n-1, ... A(2, 1) ... )) = 2^(A002487(n+1)-1). %e A357144 Array A(n, k) begins: %e A357144 n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 %e A357144 ----+------------------------------------------------------------------ %e A357144 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A357144 1 | 0 1 2 3 4 5 6 7 8 9 10 11 12 %e A357144 2 | 0 2 8 1 32 14 4 5 128 6 56 17 16 %e A357144 3 | 0 3 1 15 6 7 9 63 2 27 33 31 30 %e A357144 4 | 0 4 32 6 256 2 48 1 2048 60 16 62 384 %e A357144 5 | 0 5 14 7 2 35 1 47 20 3 1022 119 10 %e A357144 6 | 0 6 4 9 48 1 60 3 32 510 12 13 72 %e A357144 7 | 0 7 5 63 1 47 3 511 14 15 61 383 33 %e A357144 8 | 0 8 128 2 2048 20 32 14 32768 4 320 26 512 %e A357144 9 | 0 9 6 27 60 3 510 15 4 93 30 39 258 %e A357144 10 | 0 10 56 33 16 1022 12 61 320 30 196 5 1008 %e A357144 11 | 0 11 17 31 62 119 13 383 26 39 5 575 1 %e A357144 12 | 0 12 16 30 384 10 72 33 512 258 1008 1 960 %o A357144 (PARI) See Links section. %Y A357144 Cf. A002487, A054429, A354522, A355090. %K A357144 nonn,tabl %O A357144 0,8 %A A357144 _Rémy Sigrist_, Sep 15 2022