A194071 Natural interspersion of A194069; a rectangular array, by antidiagonals.

1, 3, 2, 7, 4, 5, 11, 8, 9, 6, 17, 12, 13, 10, 15, 25, 18, 19, 14, 21, 16, 33, 26, 27, 20, 29, 22, 23, 43, 34, 35, 28, 37, 30, 31, 24, 55, 44, 45, 36, 47, 38, 39, 32, 41, 67, 56, 57, 46, 59, 48, 49, 40, 51, 42, 81, 68, 69, 58, 71, 60, 61, 50, 63, 52, 53, 97, 82, 83

Offset

1,2

Comments

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, A194071 is a permutation of the positive integers; its inverse is A194072.

Links

Table of n, a(n) for n=1..69.

Example

Northwest corner:
1...3...7...11...17
2...4...8...12...18
5...9...13..19...27
6...10..14..20...28
15..21..29..37...47

Mathematica

z = 70;
c[k_] := 1 + Floor[(2/3) k^2];
c = Table[c[k], {k, 1, z}]  (* A194069 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194070 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194071 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194072 *)

Crossrefs

Cf. A194029, A194069, A194070, A194072.

Sequence in context: A153154 A154438 A354367 * A194104 A277679 A108644

Adjacent sequences: A194068 A194069 A194070 * A194072 A194073 A194074

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 14 2011

Status

approved