A195083 Interspersion fractally induced by (1+[2*n/3]), where [ ] = floor; a rectangular array, by antidiagonals.

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

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, A195082, 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