This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A136272 #13 Jul 19 2024 11:33:10 %S A136272 1,3,6,7,11,12,13,18,19,20,21,27,28,29,30,31,38,39,40,41,42,43,51,52, %T A136272 53,54,55,56,57,66,67,68,69,70,71,72,73,83,84,85,86,87,88,89,90,91, %U A136272 102,103,104,105,106,107,108,109,110,111,123,124,125,126,127,128,129 %N A136272 Waterbird take-off sequence. Complement of A166021. %C A136272 This kind of sequence can be generalized as follows: %C A136272 Let F(t), G(t) be arithmetic functions: F(t) the right hand move, G(t) the number of erased positions. %C A136272 Then starting from the position t=1 do procedure: %C A136272 JUMP F(t) positions right hand %C A136272 ERASE G(t) positions %C A136272 SET t=t+1 %C A136272 repeat procedure from the last erased position. %C A136272 This sequence has F(t)=t, G(t)=t. %C A136272 We can use a set of functions F_i(t) and G_i(t) processed in parallel (a flock of birds taking off). %H A136272 D. X. Charles, <a href="http://pages.cs.wisc.edu/~cdx/Sieve.pdf">Sieve Methods</a>, July 2000, University of Wisconsin. %H A136272 R. Eismann, <a href="http://arxiv.org/abs/0711.0865">Decomposition of natural numbers into weight X level + jump and application to a new classification of prime numbers</a>, arXiv:0711.0865 [math.NT], 2007-2010. %H A136272 M. C. Wunderlich, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1614.pdf">A general class of sieve generated sequences</a>, Acta Arithmetica XVI,1969, pp. 41-56. %F A136272 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*). %e A136272 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,... %e A136272 t=1; from the position 1 go 1 position to the right, erase 1 position: %e A136272 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,... %e A136272 t=2; from the last erased position go 2 positions to the right, erase 2 positions: %e A136272 1..3..,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,... %e A136272 t=3; from the last erased position go 3 positions to the right, erase 3 positions: %e A136272 1..3..,6,7....11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,... %e A136272 t=4; from the last erased position go 4 positions to the right, erase 4 positions: %e A136272 1..3..,6,7....11,12,13....,18,19,20,21,22,23,24,25,26,27,... %e A136272 t=5; from the last erased position go 5 positions to the right, erase 5 positions: %e A136272 1..3..,6,7....11,12,13....,18,19,20,21......27,... %e A136272 The erased positions form the complement of this sequence: A166021. %o A136272 (PARI) is_A136272(n) = if(n<3, n==1, my(s=sqrtint(n-2)); n-2 < s*(s+1)) \\ _Hugo Pfoertner_, Jul 19 2024 %Y A136272 Cf. A004202, A064801, A137292. %K A136272 easy,nonn %O A136272 1,2 %A A136272 _Ctibor O. Zizka_, Mar 19 2008 %E A136272 Edited and corrected by _Antti Karttunen_, Oct 05 2009