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A194104 Natural interspersion of A194102; a rectangular array, by antidiagonals.

%I A194104 #5 Mar 30 2012 18:57:40
%S A194104 1,3,2,7,4,5,12,8,9,6,19,13,14,10,11,27,20,21,15,16,17,36,28,29,22,23,
%T A194104 24,18,47,37,38,30,31,32,25,26,59,48,49,39,40,41,33,34,35,73,60,61,50,
%U A194104 51,52,42,43,44,45,88,74,75,62,63,64,53,54,55,56,46,104,89,90
%N A194104 Natural interspersion of A194102; a rectangular array, by antidiagonals.
%C A194104 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, A194100 is a permutation of the positive integers; its inverse is A194101.
%e A194104 Northwest corner:
%e A194104 1...3...7...12...19
%e A194104 2...4...8...13...20
%e A194104 5...9...14..21...29
%e A194104 6...10..15..22...30
%e A194104 11..16..23..31...40
%t A194104 z = 40; g = Sqrt[2];
%t A194104 c[k_] := Sum[Floor[j*g], {j, 1, k}];
%t A194104 c = Table[c[k], {k, 1, z}]  (* A194102 *)
%t A194104 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194104 f = Table[f[n], {n, 1, 800}]  (* A194103  new *)
%t A194104 r[n_] := Flatten[Position[f, n]]
%t A194104 t[n_, k_] := r[n][[k]]
%t A194104 TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
%t A194104 p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194104 *)
%t A194104 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194105 *)
%Y A194104 Cf. A194029, A194102, A194103, A194105.
%K A194104 nonn,tabl
%O A194104 1,2
%A A194104 _Clark Kimberling_, Aug 15 2011