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A136272 Waterbird take-off sequence. Complement of A166021. 9
1, 3, 6, 7, 11, 12, 13, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 51, 52, 53, 54, 55, 56, 57, 66, 67, 68, 69, 70, 71, 72, 73, 83, 84, 85, 86, 87, 88, 89, 90, 91, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 123, 124, 125, 126, 127, 128, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This kind of sequence can be generalized as follows:

Let F(t), G(t) be arithmetic functions: F(t) the right hand move, G(t) the number of erased positions.

Then starting from the position t=1 do procedure:

JUMP F(t) positions right hand

ERASE G(t) positions

SET t=t+1

repeat procedure from the last erased position.

This sequence has F(t)=t, G(t)=t.

We can use a set of functions F_i(t) and G_i(t) processed in parallel (a flock of birds taking off).

LINKS

Table of n, a(n) for n=1..63.

D. X. Charles, Sieve Methods, July 2000, University of Wisconsin.

R. Eismann, Decomposition of natural numbers into weight X level + jump and application to a new classification of prime numbers, arXiv:0711.0865 [math.NT], 2007-2010.

M. C. Wunderlich, A general class of sieve generated sequences, Acta Arithmetica XVI,1969, pp. 41-56.

FORMULA

a(0)=1; let t=1. Start on position t. Jump t positions right hand. Erase t positions. (*P*) Set t=t+1. Start on the last erased position. Jump t positions right hand. Erase t positions. Repeat procedure (*P*).

EXAMPLE

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,...

t=1; from the position 1 go 1 position to the right, erase 1 position:

1..3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,...

t=2; from the last erased position go 2 positions to the right, erase 2 positions:

1..3..,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,...

t=3; from the last erased position go 3 positions to the right, erase 3 positions:

1..3..,6,7....11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,...

t=4; from the last erased position go 4 positions to the right, erase 4 positions:

1..3..,6,7....11,12,13....,18,19,20,21,22,23,24,25,26,27,...

t=5; from the last erased position go 5 positions to the right, erase 5 positions:

1..3..,6,7....11,12,13....,18,19,20,21......27,...

The erased positions form the complement of this sequence: A166021.

CROSSREFS

Cf. A137292.

Sequence in context: A004780 A292046 A051146 * A101184 A087643 A248150

Adjacent sequences: A136269 A136270 A136271 * A136273 A136274 A136275

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Mar 19 2008

EXTENSIONS

Edited and corrected by Antti Karttunen, Oct 05 2009

STATUS

approved

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Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)