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

Author

Clark Kimberling, Aug 13 2011

Keywords

• nonn
• tabl

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.

Examples

			 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
		

Crossrefs

Cf. A194029, A194047

Programs

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 *)