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A195083 Interspersion fractally induced by (1+[2n/3]), where [ ] = floor; a rectangular array, by antidiagonals. 3
1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 15, 13, 14, 16, 17, 21, 18, 19, 20, 22, 23, 28, 24, 25, 27, 26, 29, 30, 36, 31, 32, 35, 33, 34, 37, 38, 45, 39, 40, 44, 41, 42, 43, 46, 47, 55, 48, 49, 54, 50, 51, 53, 52, 56, 57, 66, 58, 59, 65, 60, 61, 64, 62, 63, 67, 68, 78 (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, A194983 is a permutation of the positive integers, with inverse A195096.

LINKS

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

EXAMPLE

Northwest corner:

1...2...4...7...11..16

3...5...8...12..17..23

6...10..15..21..28..36

9...13..18..24..31..39

14..19..25..32..40..49

MATHEMATICA

r = 2/3; p[n_] := 1 + Floor[n*r]

Table[p[n], {n, 1, 90}]  (* ess A004396 *)

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] (* A195082 *)

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}]] (* A195083 *)

q[n_] := Position[w, n]; Flatten[Table[q[n],

{n, 1, 80}]] (* A195096 *)

CROSSREFS

Cf. A004396, A195083, A195096.

Sequence in context: A194978 A195096 A194977 * A073294 A073295 A191656

Adjacent sequences:  A195080 A195081 A195082 * A195084 A195085 A195086

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 08 2011

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)