A194100 - OEIS

%I #6 Mar 30 2012 18:57:39

%S 1,6,2,13,7,3,23,14,8,4,36,24,15,9,5,51,37,25,16,10,11,69,52,38,26,17,

%T 18,12,89,70,53,39,27,28,19,20,112,90,71,54,40,41,29,30,21,138,113,91,

%U 72,55,56,42,43,31,22,166,139,114,92,73,74,57,58,44,32,33,197

%N Natural interspersion of A194126; 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, A194100 is a permutation of the positive integers; its inverse is A194101.

%e Northwest corner:

%e 1...6...13...23...36

%e 2...7...14...24...37

%e 3...8...15...25...38

%e 4...9...16...26...39

%e 5...10..17...27...40

%e 11..18..28...41...56

%t z = 40; g = GoldenRatio;

%t c[k_] := -1 + Sum[Floor[j + j*g], {j, 1, k}];

%t c = Table[c[k], {k, 1, z}]  (* 194126 *)

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

%t f = Table[f[n], {n, 1, 800}]  (* A193042 *)

%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}]]  (* A194100 *)

%t q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194101 *)

%Y Cf. A194029, A194126, A193042, A194101.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 15 2011