A194833 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194832; an interspersion.

1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 12, 14, 11, 13, 15, 18, 20, 16, 19, 21, 17, 24, 27, 22, 25, 28, 23, 26, 32, 35, 30, 33, 36, 31, 34, 29, 40, 44, 38, 42, 45, 39, 43, 37, 41, 49, 53, 47, 51, 55, 48, 52, 46, 50, 54, 60, 64, 57, 62, 66, 59, 63, 56, 61, 65, 58, 71, 76, 68

Offset: 1

Author

Clark Kimberling, Sep 03 2011

Keywords

• nonn
• tabl

Comments

As a sequence, A194833 is a permutation of the positive integers; its inverse is A194834.

Examples

			Northwest corner:
1...2...5...8...12..18..24
3...6...10..14..20..27..35
4...7...11..16..22..30..38
9...13..19..25..33..42..51
15..21..28..36..45..55..66
		

Crossrefs

Cf. A194832, A194834.

Programs

Mathematica

r = -GoldenRatio;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]
(* A194832 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A194833 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]] (* A194834 *)