A194912 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194905; an interspersion.

1, 2, 3, 4, 5, 6, 8, 9, 10, 7, 12, 14, 15, 11, 13, 17, 19, 21, 16, 18, 20, 23, 25, 27, 22, 24, 26, 28, 31, 33, 35, 29, 32, 34, 36, 30, 39, 42, 44, 37, 40, 43, 45, 38, 41, 48, 51, 54, 46, 49, 52, 55, 47, 50, 53, 58, 61, 64, 56, 59, 62, 65, 57, 60, 63, 66, 70, 73, 76

Offset

1,2

Comments

See A194832 for a general discussion. A194912 is not equal to A194842.

Links

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

Example

Northwest corner:
1...2...4...8...12..17
3...5...9...14..19..25
6...10..15..21..27..35
7...11..16..22..29..37
13..18..24..32..40..49

Mathematica

r = 2^(1/3);
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]]  (* A194911 *)
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}]]  (* A194912 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194913 *)

Crossrefs

Cf. A194832, A194911, A194913.

Sequence in context: A303595 A195184 A194842 * A194866 A345254 A004726

Adjacent sequences: A194909 A194910 A194911 * A194913 A194914 A194915

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 05 2011

Status

approved