A194038 Natural interspersion of A034856, a rectangular array, by antidiagonals.

1, 4, 2, 8, 5, 3, 13, 9, 6, 7, 19, 14, 10, 11, 12, 26, 20, 15, 16, 17, 18, 34, 27, 21, 22, 23, 24, 25, 43, 35, 28, 29, 30, 31, 32, 33, 53, 44, 36, 37, 38, 39, 40, 41, 42, 64, 54, 45, 46, 47, 48, 49, 50, 51, 52, 76, 65, 55, 56, 57, 58, 59, 60, 61, 62, 63, 89, 77, 66

Offset

0,2

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, A194038 is a permutation of the positive integers; its inverse is A194040.

Links

Table of n, a(n) for n=0..68.

Example

Northwest corner:
1...4...8...13...19
2...5...9...14...20
3...6...10..15...21
7...11..16..22...29
12..17..23..30...38

Mathematica

z = 30;
c[k_] := (k^2 + 3 k - 2)/2;
c = Table[c[k], {k, 1, z}]  (* A034856 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 255}]  (* essentially A002260 *)
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, 13}, {k, 1, n}]]   (* A194038 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194040 *)

Crossrefs

Cf. A192872, A194040.

Sequence in context: A143095 A141073 A261830 * A131819 A194064 A194054

Adjacent sequences: A194035 A194036 A194037 * A194039 A194040 A194041

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 12 2011

Status

approved