A194011 Natural interspersion of A002061; a rectangular array, by antidiagonals.

1, 3, 2, 7, 4, 5, 13, 8, 9, 6, 21, 14, 15, 10, 11, 31, 22, 23, 16, 17, 12, 43, 32, 33, 24, 25, 18, 19, 57, 44, 45, 34, 35, 26, 27, 20, 73, 58, 59, 46, 47, 36, 37, 28, 29, 91, 74, 75, 60, 61, 48, 49, 38, 39, 30, 111, 92, 93, 76, 77, 62, 63, 50, 51, 40, 41, 133, 112

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, A194011 is a permutation of the positive integers; its inverse is A194012.

Links

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

Example

Northwest corner:
1...3...7...13...21...31
2...4...8...14...22...32
5...9...15..23...33...45
6...10..16..24...34...46
11..17..25..35...47...61

Mathematica

z = 40;
c[k_] := k^2 - k + 1
c = Table[c[k], {k, 1, z}]  (* A002061 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A074294 *)
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}]]  (* A194011 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194012 *)

Crossrefs

Cf. A194029, A002061, A074294, A194012.

Sequence in context: A194104 A277679 A108644 * A370698 A303763 A303765

Adjacent sequences: A194008 A194009 A194010 * A194012 A194013 A194014

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 15 2011

Status

approved