A194100 Natural interspersion of A194126; a rectangular array, by antidiagonals.

1, 6, 2, 13, 7, 3, 23, 14, 8, 4, 36, 24, 15, 9, 5, 51, 37, 25, 16, 10, 11, 69, 52, 38, 26, 17, 18, 12, 89, 70, 53, 39, 27, 28, 19, 20, 112, 90, 71, 54, 40, 41, 29, 30, 21, 138, 113, 91, 72, 55, 56, 42, 43, 31, 22, 166, 139, 114, 92, 73, 74, 57, 58, 44, 32, 33, 197

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, A194100 is a permutation of the positive integers; its inverse is A194101.

Links

Table of n, a(n) for n=1..67.

Example

Northwest corner:
1...6...13...23...36
2...7...14...24...37
3...8...15...25...38
4...9...16...26...39
5...10..17...27...40
11..18..28...41...56

Mathematica

z = 40; g = GoldenRatio;
c[k_] := -1 + Sum[Floor[j + j*g], {j, 1, k}];
c = Table[c[k], {k, 1, z}]  (* 194126 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A193042 *)
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}]]  (* A194100 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194101 *)

Crossrefs

Cf. A194029, A194126, A193042, A194101.

Sequence in context: A112591 A106034 A194036 * A332351 A142867 A080977

Adjacent sequences: A194097 A194098 A194099 * A194101 A194102 A194103

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 15 2011

Status

approved