A194034 Natural interspersion of A028387, a rectangular array, by antidiagonals.

1, 5, 2, 11, 6, 3, 19, 12, 7, 4, 29, 20, 13, 8, 9, 41, 30, 21, 14, 15, 10, 55, 42, 31, 22, 23, 16, 17, 71, 56, 43, 32, 33, 24, 25, 18, 89, 72, 57, 44, 45, 34, 35, 26, 27, 109, 90, 73, 58, 59, 46, 47, 36, 37, 28, 131, 110, 91, 74, 75, 60, 61, 48, 49, 38, 39, 155, 132

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, A194034 is a permutation of the positive integers; its inverse is A194035.

Links

Table of n, a(n) for n=1..68.

Example

Northwest corner:
1...5...11...19...29...41
2...6...12...20...30...42
3...7...13...21...31...43
4...8...14...22...32...44
9...15..23...33...45...59

Mathematica

z = 30;
c[k_] := k^2 + k - 1;
c = Table[c[k], {k, 1, z}]  (* A028387 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 255}]  (* A074294 *)
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}]]  (* A194034 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 70}]]  (* A194035 *)

Crossrefs

Cf. A194029, A194035.

Sequence in context: A051308 A257327 A074642 * A163257 A332452 A176624

Adjacent sequences: A194031 A194032 A194033 * A194035 A194036 A194037

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 12 2011

Status

approved