1,2

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).

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 2007--2009.

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

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*).

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.

Cf. A137292.

Sequence in context: A028795 A004780 A051146 this_sequence A101184 A087643 A022544

Adjacent sequences: A136269 A136270 A136271 this_sequence A136273 A136274 A136275

easy,nonn

Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 19 2008

Edited and corrected by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 05 2009