A194966 Interspersion fractally induced by A194965, a rectangular array, by antidiagonals.

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

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.

Index entries for sequences that are permutations of the natural numbers

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 (inverse).

Sequence in context: A370132 A023771 A132033 * A133137 A160543 A023810

Adjacent sequences: A194963 A194964 A194965 * A194967 A194968 A194969

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2011

Status

approved