A112382 A self-descriptive fractal sequence: the sequence contains every positive integer. If the first occurrence of each integer is deleted from the sequence, the resulting sequence is the same is the original (this process may be called "upper trimming").

1, 1, 2, 1, 3, 4, 2, 5, 1, 6, 7, 8, 3, 9, 10, 11, 12, 4, 13, 14, 2, 15, 16, 17, 18, 19, 5, 20, 1, 21, 22, 23, 24, 25, 26, 6, 27, 28, 29, 30, 31, 32, 33, 7, 34, 35, 36, 37, 38, 39, 40, 41, 8, 42, 43, 44, 3, 45, 46, 47, 48, 49, 50, 51, 52, 53, 9, 54, 55, 56, 57, 58, 59, 60

Offset

0,3

Comments

This sequence is also self-descriptive in that each element gives the number of first occurrences of integers (X's in the example) that were removed just before it.

Links

Table of n, a(n) for n=0..73.

Example

If we denote the first occurrence of each integer by X we get:
X, 1, X, 1, X, X, 2, X, 1, X, X, X, 3, X, X, X, X, 4, X, X, 2, ...
and dropping the X's:
1, 1, 2, 1, 3, 4, 2, ...
which is the beginning of the original sequence.

Mathematica

uppertrim[list_]:= Fold[DeleteCases[#1, #2, 1, 1]&, list, Range[Max[list]]]; Nest[Flatten[Append[#, Append[Range[Max[#] + 1, Max[#] + #[[Length[uppertrim[#]] + 1]]], #[[Length[uppertrim[#]] + 1]]]]] &, {1, 1}, 10] (* Birkas Gyorgy, Apr 27 2011 *)

Crossrefs

Cf. A112377, A112383, A112384.

Sequence in context: A337226 A120874 A358103 * A117384 A358799 A125160

Adjacent sequences: A112379 A112380 A112381 * A112383 A112384 A112385

Keyword

nonn

Author

Kerry Mitchell, Dec 05 2005

Status

approved