A194108 Natural interspersion of A194106; a rectangular array, by antidiagonals.

1, 4, 2, 9, 5, 3, 15, 10, 6, 7, 23, 16, 11, 12, 8, 33, 24, 17, 18, 13, 14, 45, 34, 25, 26, 19, 20, 21, 58, 46, 35, 36, 27, 28, 29, 22, 73, 59, 47, 48, 37, 38, 39, 30, 31, 90, 74, 60, 61, 49, 50, 51, 40, 41, 32, 109, 91, 75, 76, 62, 63, 64, 52, 53, 42, 43, 129, 110

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, A194108 is a permutation of the positive integers; its inverse is A194109.

Links

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

Example

Northwest corner:
1...4...9...15...23
2...5...10..16...24
3...6...11..17...25
7...12..18..26...36
8...13..19..27...37

Mathematica

z = 40; g = Sqrt[3];
c[k_] := Sum[Floor[j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}]  (* A194106 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A194107 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 8}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 16}, {k, 1, n}]]  (* A194108 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194109 *)

Crossrefs

Cf. A194029, A194106, A194107, A194109.

Sequence in context: A262025 A118013 A157647 * A091452 A194032 A191739

Adjacent sequences: A194105 A194106 A194107 * A194109 A194110 A194111

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 15 2011

Status

approved