A194046 Natural interspersion of A052905, a rectangular array, by antidiagonals.

1, 5, 2, 10, 6, 3, 16, 11, 7, 4, 23, 17, 12, 8, 9, 31, 24, 18, 13, 14, 15, 40, 32, 25, 19, 20, 21, 22, 50, 41, 33, 26, 27, 28, 29, 30, 61, 51, 42, 34, 35, 36, 37, 38, 39, 73, 62, 52, 43, 44, 45, 46, 47, 48, 49, 86, 74, 63, 53, 54, 55, 56, 57, 58, 59, 60, 100, 87, 75

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, A194046 is a permutation of the positive integers; its inverse is A194047.

Links

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

Example

 Northwest corner:
1...5...10...16...23
2...6...11...17...24
3...7...12...18...25
4...8...13...19...26
9...14..20...27...35

Mathematica

z = 30;
c[k_] := (k^2 + 5 k - 4)/2;
c = Table[c[k], {k, 1, z}]  (* A052905 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 255}]  (* fractal sequence [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}]]  (* A194046 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]] (* A194047 *)

Crossrefs

Cf. A194029, A194047

Sequence in context: A178714 A036121 A162396 * A249368 A055682 A187875

Adjacent sequences: A194043 A194044 A194045 * A194047 A194048 A194049

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 13 2011

Status

approved