A194969 Interspersion fractally induced by A194968, a rectangular array, by antidiagonals.

1, 2, 3, 4, 6, 5, 7, 10, 8, 9, 11, 15, 12, 13, 14, 16, 21, 17, 18, 20, 19, 22, 28, 23, 24, 27, 25, 26, 29, 36, 30, 31, 35, 32, 34, 33, 37, 45, 38, 39, 44, 40, 43, 41, 42, 46, 55, 47, 48, 54, 49, 53, 50, 51, 52, 56, 66, 57, 58, 65, 59, 64, 60, 61, 63, 62, 67, 78, 68

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, A194969 is a permutation of the positive integers, with inverse A194970.

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...6...10..15..21..28
5...8...12..17..23..30
9...13..18..24..31..39
14..20..27..35..44..54

Mathematica

r = GoldenRatio; p[n_] := 1 + Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A019446 *)
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]  (* A194968 *)
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}]]  (* A194969 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194970 *)

Crossrefs

Cf. A194958, A019446, A194968, A194970 (inverse).

Sequence in context: A064578 A371247 A361251 * A194981 A057027 A371246

Adjacent sequences: A194966 A194967 A194968 * A194970 A194971 A194972

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2011

Status

approved