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A195083 Interspersion fractally induced by (1+[2*n/3]), where [ ] = floor; a rectangular array, by antidiagonals.

%I A195083 #9 Jun 26 2025 07:30:40
%S A195083 1,2,3,4,5,6,7,8,10,9,11,12,15,13,14,16,17,21,18,19,20,22,23,28,24,25,
%T A195083 27,26,29,30,36,31,32,35,33,34,37,38,45,39,40,44,41,42,43,46,47,55,48,
%U A195083 49,54,50,51,53,52,56,57,66,58,59,65,60,61,64,62,63,67,68,78
%N A195083 Interspersion fractally induced by (1+[2*n/3]), where [ ] = floor; a rectangular array, by antidiagonals.
%C A195083 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence. Every pair of rows eventually intersperse. As a sequence, A194983 is a permutation of the positive integers, with inverse A195096.
%e A195083 Northwest corner:
%e A195083   1   2   4   7   11  16
%e A195083   3   5   8   12  17  23
%e A195083   6   10  15  21  28  36
%e A195083   9   13  18  24  31  39
%e A195083   14  19  25  32  40  49
%t A195083 r = 2/3; p[n_] := 1 + Floor[n*r]
%t A195083 Table[p[n], {n, 1, 90}]  (* ess A004396 *)
%t A195083 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195083 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195083 f[20] (* A195082 *)
%t A195083 row[n_] := Position[f[30], n];
%t A195083 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195083 v[n_, k_] := Part[row[n], k];
%t A195083 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A195083 *)
%t A195083 q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A195096 *)
%Y A195083 Cf. A004396, A195082, A195096.
%K A195083 nonn,tabl
%O A195083 1,2
%A A195083 _Clark Kimberling_, Sep 08 2011