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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)