1,2

Waterbird take-off sequence generalized :

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. http://pages.cs.wisc.edu/~cdx/Sieve.pdf

R. Eismann : Decomposition of natural numbers into weight X level + jump and application to a new classification of prime numbers, ArXiv 2008. http://arXiv.org/PS_cache/arXiv/pdf/0711/0711.0865v2.pdf

M. C. Wunderlich : Ageneral class of sieve generated sequences, Acta Arithmetica XVI,1969, pp.41-56. http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1614.pdf

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,...

Cf. A137292.

Adjacent sequences: A136269 A136270 A136271 this_sequence A136273 A136274 A136275

Sequence in context: A028795 A004780 A051146 this_sequence A101184 A087643 A022544

easy,nonn,uned

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