A194077 Natural interspersion of A060432; a rectangular array, by antidiagonals.

1, 3, 2, 5, 4, 7, 8, 6, 10, 17, 11, 9, 13, 21, 34, 14, 12, 16, 25, 39, 60, 18, 15, 20, 29, 44, 66, 97, 22, 19, 24, 33, 49, 72, 104, 147, 26, 23, 28, 38, 54, 78, 111, 155, 212, 30, 27, 32, 43, 59, 84, 118, 163, 221, 294, 35, 31, 37, 48, 65, 90, 125, 171, 230, 304

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, A194077 is a permutation of the positive integers; its inverse is A194078.

Links

Table of n, a(n) for n=1..65.

Example

Northwest corner:
1...3...5...8...11...14
2...4...6...9...12...15
7...10..13..16..20...24
17..21..25..29..33..38
34..39..44..49..54..59

Mathematica

z = 70;
c[k_] := Sum[Floor[1/2 + Sqrt[2 j]], {j, 0, k}];
c = Table[c[k], {k, 1, z}]  (* A060432 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 600}]   (* [A121997] *)
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, 12}, {k, 1, n}]] (* A194077 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]]   (* A194078 *)

Crossrefs

Cf. A194029, A060432, A194078

Sequence in context: A270197 A332769 A191709 * A257334 A137707 A164380

Adjacent sequences: A194074 A194075 A194076 * A194078 A194079 A194080

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 14 2011

Status

approved