A194030 Natural interspersion of the Fibonacci sequence (1,2,3,5,8,...), a rectangular array, by antidiagonals.

1, 2, 4, 3, 6, 7, 5, 9, 10, 11, 8, 14, 15, 16, 12, 13, 22, 23, 24, 17, 18, 21, 35, 36, 37, 25, 26, 19, 34, 56, 57, 58, 38, 39, 27, 20, 55, 90, 91, 92, 59, 60, 40, 28, 29, 89, 145, 146, 147, 93, 94, 61, 41, 42, 30, 144, 234, 235, 236, 148, 149, 95, 62, 63, 43, 31

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, this sequence is a permutation of the positive integers; its inverse is A194031.

Links

Table of n, a(n) for n=1..66.

Index entries for sequences that are permutations of the natural numbers

Example

Northwest corner:
1...2...3...5...8...13
4...6...9...14..22..35
7...10..15..23..36..57
11..16..24..37..58..92
12..17..25..38..59..93

Mathematica

z = 40;
c[k_] := Fibonacci[k + 1];
c = Table[c[k], {k, 1, z}]  (* A000045 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 800}]  (* A194029 *)
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, 13}, {k, 1, n}]]  (* A194030 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A194031 *)

Crossrefs

Cf. A194029, A194031 (inverse).

Column 1 appears to be A345347.

Sequence in context: A297551 A297673 A083050 * A353658 A083044 A361995

Adjacent sequences: A194027 A194028 A194029 * A194031 A194032 A194033

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 12 2011

Status

approved