A194036 Natural interspersion of A028872, a rectangular array, by antidiagonals.

1, 6, 2, 13, 7, 3, 22, 14, 8, 4, 33, 23, 15, 9, 5, 46, 34, 24, 16, 10, 11, 61, 47, 35, 25, 17, 18, 12, 78, 62, 48, 36, 26, 27, 19, 20, 97, 79, 63, 49, 37, 38, 28, 29, 21, 118, 98, 80, 64, 50, 51, 39, 40, 30, 31, 141, 119, 99, 81, 65, 66, 52, 53, 41, 42, 32, 166, 142

Offset: 1

Author

Clark Kimberling, Aug 12 2011

Keywords

• nonn
• tabl

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, A194036 is a permutation of the positive integers; its inverse is A194037.

Examples

			Northwest corner:
1...6...13...22...33
2...7...14...23...34
3...8...15...24...35
4...9...16...25...36
5...10..17...26...37
11..18..27...38...51
		

Crossrefs

Cf. A192872, A194037.

Programs

Mathematica

z = 30;
c[k_] := k^2 + 2 k - 2;
c = Table[c[k], {k, 1, z}]  (* A028872 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 255}]  (* A071797 *)
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, 13}, {k, 1, n}]]  (* A194036 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194037 *)