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
Offset: 1
Examples
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.
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.
Programs
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PARI
is_A136272(n) = if(n<3, n==1, my(s=sqrtint(n-2)); n-2 < s*(s+1)) \\ Hugo Pfoertner, Jul 19 2024
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*).
Extensions
Edited and corrected by Antti Karttunen, Oct 05 2009
Comments