A136272 - OEIS

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A136272

Waterbird take-off sequence. Complement of A166021.

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; 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	`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.`
	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: A028795 A004780 A051146 * A101184 A087643 A022544` `Adjacent sequences: A136269 A136270 A136271 * A136273 A136274 A136275`
	KEYWORD	`easy,nonn`
	AUTHOR	`Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 19 2008`
	EXTENSIONS	`Edited and corrected by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 05 2009`

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Last modified February 17 11:35 EST 2012. Contains 206011 sequences.