cp's OEIS Frontend

A194038 Natural interspersion of A034856, a rectangular array, by antidiagonals.

%I A194038 #6 Mar 30 2012 18:57:39
%S A194038 1,4,2,8,5,3,13,9,6,7,19,14,10,11,12,26,20,15,16,17,18,34,27,21,22,23,
%T A194038 24,25,43,35,28,29,30,31,32,33,53,44,36,37,38,39,40,41,42,64,54,45,46,
%U A194038 47,48,49,50,51,52,76,65,55,56,57,58,59,60,61,62,63,89,77,66
%N A194038 Natural interspersion of A034856, a rectangular array, by antidiagonals.
%C A194038 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, A194038 is a permutation of the positive integers; its inverse is A194040.
%e A194038 Northwest corner:
%e A194038 1...4...8...13...19
%e A194038 2...5...9...14...20
%e A194038 3...6...10..15...21
%e A194038 7...11..16..22...29
%e A194038 12..17..23..30...38
%t A194038 z = 30;
%t A194038 c[k_] := (k^2 + 3 k - 2)/2;
%t A194038 c = Table[c[k], {k, 1, z}]  (* A034856 *)
%t A194038 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194038 f = Table[f[n], {n, 1, 255}]  (* essentially A002260 *)
%t A194038 r[n_] := Flatten[Position[f, n]]
%t A194038 t[n_, k_] := r[n][[k]]
%t A194038 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194038 p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]   (* A194038 *)
%t A194038 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194040 *)
%Y A194038 Cf. A192872, A194040.
%K A194038 nonn,tabl
%O A194038 0,2
%A A194038 _Clark Kimberling_, Aug 12 2011