

A112382


A selfdescriptive 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").


3



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
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OFFSET

0,3


COMMENTS

This sequence is also selfdescriptive 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: A107893 A131987 A120874 * A117384 A125160 A009947
Adjacent sequences: A112379 A112380 A112381 * A112383 A112384 A112385


KEYWORD

nonn


AUTHOR

Kerry Mitchell, Dec 05 2005


STATUS

approved



