A195111 Interspersion fractally induced by the fractal sequence A002260.

1, 3, 2, 6, 4, 5, 10, 8, 9, 7, 15, 13, 14, 11, 12, 21, 19, 20, 16, 17, 18, 28, 26, 27, 23, 24, 25, 22, 36, 34, 35, 31, 32, 33, 29, 30, 45, 43, 44, 40, 41, 42, 37, 38, 39, 55, 53, 54, 50, 51, 52, 46, 47, 48, 49, 66, 64, 65, 61, 62, 63, 57, 58, 59, 60, 56, 78, 76, 77

Offset: 1

Author

Clark Kimberling, Sep 09 2011

Keywords

• nonn
• tabl

Comments

See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.

Every pair of rows eventually intersperse. As a sequence, A194111 is a permutation of the positive integers, with inverse A195129.

The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

Examples

			Northwest corner:
1...3...6...10..15..21..28..36..45
2...4...8...13..19..26..34..43..53
5...9...14..20..27..35..44..54..65
7...11..16..23..31..40..50..61..73
12..17..24..32..41..51..62..74..87
		

Crossrefs

Cf. A194959, A002260, A195110, A195112.

Programs

Mathematica

j[n_] := Table[k, {k, 1, n}]; t[1] = j[1];
t[n_] := Join[t[n - 1], j[n]]   (* A002260 *)
t[12]
p[n_] := t[20][[n]]
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20] (* A195110 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
  {k, 1, n}]] (* A195111 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
  {n, 1, 80}]]  (* A195112 *)