cp's OEIS Frontend

A194036 Natural interspersion of A028872, a rectangular array, by antidiagonals.

%I A194036 #5 Mar 30 2012 18:57:39
%S A194036 1,6,2,13,7,3,22,14,8,4,33,23,15,9,5,46,34,24,16,10,11,61,47,35,25,17,
%T A194036 18,12,78,62,48,36,26,27,19,20,97,79,63,49,37,38,28,29,21,118,98,80,
%U A194036 64,50,51,39,40,30,31,141,119,99,81,65,66,52,53,41,42,32,166,142
%N A194036 Natural interspersion of A028872, a rectangular array, by antidiagonals.
%C A194036 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, A194036 is a permutation of the positive integers; its inverse is A194037.
%e A194036 Northwest corner:
%e A194036 1...6...13...22...33
%e A194036 2...7...14...23...34
%e A194036 3...8...15...24...35
%e A194036 4...9...16...25...36
%e A194036 5...10..17...26...37
%e A194036 11..18..27...38...51
%t A194036 z = 30;
%t A194036 c[k_] := k^2 + 2 k - 2;
%t A194036 c = Table[c[k], {k, 1, z}]  (* A028872 *)
%t A194036 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194036 f = Table[f[n], {n, 1, 255}]  (* A071797 *)
%t A194036 r[n_] := Flatten[Position[f, n]]
%t A194036 t[n_, k_] := r[n][[k]]
%t A194036 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194036 p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194036 *)
%t A194036 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194037 *)
%Y A194036 Cf. A192872, A194037.
%K A194036 nonn,tabl
%O A194036 1,2
%A A194036 _Clark Kimberling_, Aug 12 2011