A194839 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194838; an interspersion.

1, 3, 2, 6, 5, 4, 9, 8, 7, 10, 14, 12, 11, 15, 13, 20, 18, 16, 21, 19, 17, 27, 25, 23, 28, 26, 24, 22, 34, 32, 30, 36, 33, 31, 29, 35, 43, 40, 38, 45, 42, 39, 37, 44, 41, 53, 50, 47, 55, 52, 49, 46, 54, 51, 48, 64, 61, 58, 66, 63, 60, 57, 65, 62, 59, 56, 75, 72, 69

Offset: 1

Author

Clark Kimberling, Sep 03 2011

Keywords

• nonn
• tabl

Comments

See A194832 and A194838.

Examples

			Northwest corner:
1...3...6...9...14..20..27
2...5...8...12..18..25..32
4...7...11..16..23..30..38
10..15..21..28..36..45..55
13..19..26..33..42..52..63
17..24..31..39..49..60..71
		

Crossrefs

Cf. A194838, A194840, A194832.

Programs

Mathematica

r = Sqrt[3];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]  (* A194838 *)
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}]]  (* A194839 *)
q[n_] := Position[p, n]; Flatten[
 Table[q[n], {n, 1, 80}]]  (* A194840 *)