A194061 - OEIS

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

%S 1,2,3,4,5,8,6,7,11,15,9,10,14,19,24,12,13,18,23,29,35,16,17,22,28,34,

%T 41,48,20,21,27,33,40,47,55,63,25,26,32,39,46,54,62,71,80,30,31,38,45,

%U 53,61,70,79,89,99,36,37,44,52,60,69,78,88,98,109,120

%N Natural interspersion of A002620; 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, A194061 is a permutation of the positive integers; its inverse is A194062.

%e Northwest corner:

%e 1...2...4...6...9...12

%e 3...5...7...10..13..17

%e 8...11..14..18..22..27

%e 15..19..23..28..33..39

%e 24..29..34..40..46..53

%t z = 50;

%t c[k_] := Floor[((k + 1)^2)/4];

%t c = Table[c[k], {k, 1, z}]  (* A002620 *)

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

%t f = Table[f[n], {n, 1, 400}]   (* [A122197] *)

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

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

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

%t p = Flatten[

%t   Table[t[k, n - k + 1], {n, 1, 11}, {k, 1, n}]] (* A194061 *)

%t q[n_] := Position[p, n]; Flatten[

%t  Table[q[n], {n, 1, 90}]]  (* A194062 *)

%Y Cf. A194029, A002620, A122197, A194062.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 14 2011