

A195111


Interspersion fractally induced by the fractal sequence A002260.


4



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
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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



