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
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.
PROG
(PARI) is_A136272(n) = if(n<3, n==1, my(s=sqrtint(n-2)); n-2 < s*(s+1)) \\ Hugo Pfoertner, Jul 19 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Mar 19 2008
EXTENSIONS
Edited and corrected by Antti Karttunen, Oct 05 2009
STATUS
approved