A195108 Interspersion fractally induced by A004736.

1, 2, 3, 5, 6, 4, 8, 10, 7, 9, 13, 15, 11, 14, 12, 19, 21, 17, 20, 18, 16, 26, 28, 23, 27, 24, 22, 25, 34, 36, 30, 35, 32, 29, 33, 31, 43, 45, 39, 44, 41, 37, 42, 40, 38, 53, 55, 49, 54, 51, 47, 52, 50, 48, 46, 64, 66, 59, 65, 62, 57, 63, 61, 58, 56, 60, 76, 78, 71

Offset

1,2

Comments

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

The sequence A004736 is the fractal sequence obtained by concatenating the segments 1; 2,1; 3,2,1; 4,3,2,1;...

Every pair of rows of A195108 eventually intersperse.

As a sequence, A194108 is a permutation of the positive integers, with inverse A195109.

Links

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

Example

Northwest corner:
1...2...5...8...13..19..26
3...6...10..15..21..28..36
4...7...11..17..23..30..39
9...14..20..27..35..44..54
12..18..24..32..41..51..62

Mathematica

j[n_] := Table[n + 1 - k, {k, 1, n}]; t[1] = j[1];
t[n_] := Join[t[n - 1], j[n]]   (* A004736 *)
t[10]
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] (* A195107 *)
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}]] (* A195108 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]] (* A195109 *)

Crossrefs

Cf. A194959, A004736, A195107, A195109.

Sequence in context: A360600 A194863 A194833 * A054077 A194872 A194900

Adjacent sequences: A195105 A195106 A195107 * A195109 A195110 A195111

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 09 2011

Status

approved