A194075 Natural interspersion of A194073; a rectangular array, by antidiagonals.

1, 4, 2, 7, 5, 3, 13, 8, 6, 10, 19, 14, 9, 16, 11, 28, 20, 15, 22, 17, 12, 37, 29, 21, 31, 23, 18, 25, 49, 38, 30, 40, 32, 24, 34, 26, 61, 50, 39, 52, 41, 33, 43, 35, 27, 76, 62, 51, 64, 53, 42, 55, 44, 36, 46, 91, 77, 63, 79, 65, 54, 67, 56, 45, 58, 47, 109, 92, 78

Offset

1,2

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194075 is a permutation of the positive integers; its inverse is A194076.

Links

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

Example

Northwest corner:
1...4...7...13...19
2...5...8...14...20
3...6...9...15...21
10..16..22..31...40
11..17..23..32...41

Mathematica

z = 70;
c[k_] := 1 + Floor[(3/4) k^2];
c = Table[c[k], {k, 1, z}]  (* A194073 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194074 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[
  Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194075 *)
q[n_] := Position[p, n]; Flatten[
 Table[q[n], {n, 1, 90}]]  (* A194076 *)

Crossrefs

Cf. A194029, A194074, A194073, A194076.

Sequence in context: A131914 A115302 A109857 * A271479 A259927 A002560

Adjacent sequences: A194072 A194073 A194074 * A194076 A194077 A194078

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 14 2011

Status

approved