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

1,2

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;...

Links

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

Example

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

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 *)

Crossrefs

Cf. A194959, A002260, A195110, A195112.

Sequence in context: A191655 A120911 A064789 * A274315 A194059 A191427

Adjacent sequences: A195108 A195109 A195110 * A195112 A195113 A195114

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 09 2011

Status

approved