A194906 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 29, 38, 40, 41, 42, 43, 44, 45, 37, 39, 47, 49, 51, 52, 53, 54, 55, 46, 48, 50, 57, 59, 61, 63, 64, 65, 66, 56, 58, 60, 62, 68, 70, 72

Offset

1,2

Comments

See A194832 for a general discussion.

Links

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

Example

Northwest corner:
1...2...4...7...11..16..22
3...5...8...12..17..23..31
6...9...13..18..24..32..41
10..14..19..25..33..42..52
15..20..26..34..43..53..64

Mathematica

r = Pi;
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194905 *)
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}]]  (* A194906 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194907 *)

Crossrefs

Cf. A194832, A194905, A194907.

Sequence in context: A349294 A153679 A273887 * A160546 A356944 A087143

Adjacent sequences: A194903 A194904 A194905 * A194907 A194908 A194909

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 05 2011

Status

approved