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A194071 Natural interspersion of A194069; a rectangular array, by antidiagonals.

%I A194071 #5 Mar 30 2012 18:57:39
%S A194071 1,3,2,7,4,5,11,8,9,6,17,12,13,10,15,25,18,19,14,21,16,33,26,27,20,29,
%T A194071 22,23,43,34,35,28,37,30,31,24,55,44,45,36,47,38,39,32,41,67,56,57,46,
%U A194071 59,48,49,40,51,42,81,68,69,58,71,60,61,50,63,52,53,97,82,83
%N A194071 Natural interspersion of A194069; a rectangular array, by antidiagonals.
%C A194071 See A194029 for definitions of natural fractal sequence and natural interspersion.  Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194071 is a permutation of the positive integers; its inverse is A194072.
%e A194071 Northwest corner:
%e A194071 1...3...7...11...17
%e A194071 2...4...8...12...18
%e A194071 5...9...13..19...27
%e A194071 6...10..14..20...28
%e A194071 15..21..29..37...47
%t A194071 z = 70;
%t A194071 c[k_] := 1 + Floor[(2/3) k^2];
%t A194071 c = Table[c[k], {k, 1, z}]  (* A194069 *)
%t A194071 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194071 f = Table[f[n], {n, 1, 300}]   (* A194070 *)
%t A194071 r[n_] := Flatten[Position[f, n]]
%t A194071 t[n_, k_] := r[n][[k]]
%t A194071 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194071 p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194071 *)
%t A194071 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194072 *)
%Y A194071 Cf. A194029, A194069, A194070, A194072.
%K A194071 nonn,tabl
%O A194071 1,2
%A A194071 _Clark Kimberling_, Aug 14 2011