

A194966


Interspersion fractally induced by A194965, a rectangular array, by antidiagonals.


4



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 17, 22, 25, 26, 27, 28, 23, 24, 29, 33, 34, 35, 36, 30, 31, 32, 37, 42, 43, 44, 45, 38, 39, 40, 41, 46, 52, 53, 54, 55, 47, 48, 49, 50, 51, 56, 63, 64, 65, 66, 57, 59, 60, 61, 62, 58, 67, 75, 76
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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, A194966 is a permutation of the positive integers, with inverse A194967.


LINKS

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


EXAMPLE

Northwest corner:
1...2...4...7...11..16
3...5...8...12..18..25
6...9...13..19..26..34
10..14..20..27..35..44
15..21..28..36..45..55


MATHEMATICA

p[n_] := Floor[(n + 4)/5] + Mod[n  1, 5]
Table[p[n], {n, 1, 90}] (* A053824(n+5), n>=0 *)
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] (* A194965 *)
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}]] (* A194966 *)
q[n_] := Position[w, n]; Flatten[
Table[q[n], {n, 1, 80}]] (* A194967 *)


CROSSREFS

Cf. A194959, A194965, A194967.
Sequence in context: A179978 A023771 A132033 * A133137 A160543 A023810
Adjacent sequences: A194963 A194964 A194965 * A194967 A194968 A194969


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Sep 07 2011


STATUS

approved



