A195114 Interspersion fractally induced by the fractal sequence obtained by deleting the second two terms of the fractal sequence A002260.

1, 3, 2, 6, 4, 5, 10, 7, 8, 9, 15, 12, 13, 14, 11, 21, 18, 19, 20, 16, 17, 28, 25, 26, 27, 22, 23, 24, 36, 33, 34, 35, 29, 30, 31, 32, 45, 42, 43, 44, 38, 39, 40, 41, 37, 55, 52, 53, 54, 48, 49, 50, 51, 46, 47, 66, 63, 64, 65, 59, 60, 61, 62, 56, 57, 58, 78, 75, 76

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, A194114 is a permutation of the positive integers, with inverse A195115.

Links

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

Example

Northwest corner:
1...3...6...10..15..21..28
2...4...7...12..18..25..33
5...8...13..19..26..34..43
9...14..20..27..35..44..54
11..16..22..29..38..48..59

Mathematica

j[n_] := Table[k, {k, 1, n}];
t[1] = j[1]; t[2] = j[1];
t[n_] := Join[t[n - 1], j[n]] (* A002260; initial 1, 1, 2 repl by 1 *)
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]  (* A195113 *)
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}]] (* A195114 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A195115 *)

Crossrefs

Cf. A194959, A002260, A195113, A195115, A195111.

Sequence in context: A226077 A352200 A066182 * A059399 A194984 A194988

Adjacent sequences: A195111 A195112 A195113 * A195115 A195116 A195117

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 09 2011

Status

approved