A194061 Natural interspersion of A002620; a rectangular array, by antidiagonals.

1, 2, 3, 4, 5, 8, 6, 7, 11, 15, 9, 10, 14, 19, 24, 12, 13, 18, 23, 29, 35, 16, 17, 22, 28, 34, 41, 48, 20, 21, 27, 33, 40, 47, 55, 63, 25, 26, 32, 39, 46, 54, 62, 71, 80, 30, 31, 38, 45, 53, 61, 70, 79, 89, 99, 36, 37, 44, 52, 60, 69, 78, 88, 98, 109, 120

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, A194061 is a permutation of the positive integers; its inverse is A194062.

Links

Table of n, a(n) for n=1..66.

Example

Northwest corner:
1...2...4...6...9...12
3...5...7...10..13..17
8...11..14..18..22..27
15..19..23..28..33..39
24..29..34..40..46..53

Mathematica

z = 50;
c[k_] := Floor[((k + 1)^2)/4];
c = Table[c[k], {k, 1, z}]  (* A002620 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 400}]   (* [A122197] *)
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, 11}, {k, 1, n}]] (* A194061 *)
q[n_] := Position[p, n]; Flatten[
 Table[q[n], {n, 1, 90}]]  (* A194062 *)

Crossrefs

Cf. A194029, A002620, A122197, A194062.

Sequence in context: A146941 A194067 A191710 * A272616 A356419 A364775

Adjacent sequences: A194058 A194059 A194060 * A194062 A194063 A194064

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 14 2011

Status

approved