A194011 - OEIS

%I #5 Mar 30 2012 18:57:39

%S 1,3,2,7,4,5,13,8,9,6,21,14,15,10,11,31,22,23,16,17,12,43,32,33,24,25,

%T 18,19,57,44,45,34,35,26,27,20,73,58,59,46,47,36,37,28,29,91,74,75,60,

%U 61,48,49,38,39,30,111,92,93,76,77,62,63,50,51,40,41,133,112

%N Natural interspersion of A002061; a rectangular array, by antidiagonals.

%C 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, A194011 is a permutation of the positive integers; its inverse is A194012.

%e Northwest corner:

%e 1...3...7...13...21...31

%e 2...4...8...14...22...32

%e 5...9...15..23...33...45

%e 6...10..16..24...34...46

%e 11..17..25..35...47...61

%t z = 40;

%t c[k_] := k^2 - k + 1

%t c = Table[c[k], {k, 1, z}]  (* A002061 *)

%t f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]

%t f = Table[f[n], {n, 1, 800}]  (* A074294 *)

%t r[n_] := Flatten[Position[f, n]]

%t t[n_, k_] := r[n][[k]]

%t TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]

%t p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194011 *)

%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194012 *)

%Y Cf. A194029, A002061, A074294, A194012.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 15 2011