cp's OEIS Frontend

A194046 Natural interspersion of A052905, a rectangular array, by antidiagonals.

%I A194046 #6 Mar 30 2012 18:57:39
%S A194046 1,5,2,10,6,3,16,11,7,4,23,17,12,8,9,31,24,18,13,14,15,40,32,25,19,20,
%T A194046 21,22,50,41,33,26,27,28,29,30,61,51,42,34,35,36,37,38,39,73,62,52,43,
%U A194046 44,45,46,47,48,49,86,74,63,53,54,55,56,57,58,59,60,100,87,75
%N A194046 Natural interspersion of A052905, a rectangular array, by antidiagonals.
%C A194046 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, A194046 is a permutation of the positive integers; its inverse is A194047.
%e A194046  Northwest corner:
%e A194046 1...5...10...16...23
%e A194046 2...6...11...17...24
%e A194046 3...7...12...18...25
%e A194046 4...8...13...19...26
%e A194046 9...14..20...27...35
%t A194046 z = 30;
%t A194046 c[k_] := (k^2 + 5 k - 4)/2;
%t A194046 c = Table[c[k], {k, 1, z}]  (* A052905 *)
%t A194046 f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
%t A194046 f = Table[f[n], {n, 1, 255}]  (* fractal sequence [A002260] *)
%t A194046 r[n_] := Flatten[Position[f, n]]
%t A194046 t[n_, k_] := r[n][[k]]
%t A194046 TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
%t A194046 p = Flatten[Table[t[k, n - k + 1], {n, 1, 13}, {k, 1, n}]]  (* A194046 *)
%t A194046 q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194047 *)
%Y A194046 Cf. A194029, A194047
%K A194046 nonn,tabl
%O A194046 1,2
%A A194046 _Clark Kimberling_, Aug 13 2011