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

1,2

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

Links

Table of n, a(n) for n=1..68.

Example

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

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 *)

Crossrefs

Cf. A192872, A194037.

Sequence in context: A015808 A112591 A106034 * A194100 A332351 A142867

Adjacent sequences: A194033 A194034 A194035 * A194037 A194038 A194039

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 12 2011

Status

approved