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A194077 Natural interspersion of A060432; a rectangular array, by antidiagonals.

%I A194077 #5 Mar 30 2012 18:57:39
%S A194077 1,3,2,5,4,7,8,6,10,17,11,9,13,21,34,14,12,16,25,39,60,18,15,20,29,44,
%T A194077 66,97,22,19,24,33,49,72,104,147,26,23,28,38,54,78,111,155,212,30,27,
%U A194077 32,43,59,84,118,163,221,294,35,31,37,48,65,90,125,171,230,304
%N A194077 Natural interspersion of A060432; a rectangular array, by antidiagonals.
%C A194077 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, A194077 is a permutation of the positive integers; its inverse is A194078.
%e A194077 Northwest corner:
%e A194077 1...3...5...8...11...14
%e A194077 2...4...6...9...12...15
%e A194077 7...10..13..16..20...24
%e A194077 17..21..25..29..33..38
%e A194077 34..39..44..49..54..59
%t A194077 z = 70;
%t A194077 c[k_] := Sum[Floor[1/2 + Sqrt[2 j]], {j, 0, k}];
%t A194077 c = Table[c[k], {k, 1, z}]  (* A060432 *)
%t A194077 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194077 f = Table[f[n], {n, 1, 600}]   (* [A121997] *)
%t A194077 r[n_] := Flatten[Position[f, n]]
%t A194077 t[n_, k_] := r[n][[k]]
%t A194077 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194077 p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194077 *)
%t A194077 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]   (* A194078 *)
%Y A194077 Cf. A194029, A060432, A194078
%K A194077 nonn,tabl
%O A194077 1,2
%A A194077 _Clark Kimberling_, Aug 14 2011