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

Author

Clark Kimberling, Sep 07 2011

Keywords

• nonn
• tabl

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.

Examples

			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
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

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 *)