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 A050132 #16 Oct 15 2019 11:51:37 %S A050132 1,6,3,12,15,7,21,10,5,2,33,16,8,4,45,22,11,54,27,13,63,31,69,34,17, %T A050132 78,39,19,9,90,93,46,23,102,51,25,111,55,117,58,29,14,129,64,32,138, %U A050132 141,70,35,150,75,37,18,162,81,40,20,174,87,43 %N A050132 a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 3*n. %C A050132 This sequence is a permutation of the natural numbers. Sketch of proof: that it is one-to-one is trivial. Inductively, the halving operation can never happen more than 4 times in a row. There are at least 5 multiples of 3 amongst 16m .. 16m+15; by the induction, one of these will be a value a(n) = 3n and then 4 halving operations will get m (if it has not previously appeared). It follows that m will occur in the sequence no later than floor((16m+26)/3). Empirically, it appears that the 26 in this formula could be replaced by 21. The first occurrence of 4 consecutive halvings starts at n = 226, winding up with a(230)=42. - _Franklin T. Adams-Watters_, Mar 10 2006 %Y A050132 Cf. A050000. %K A050132 nonn %O A050132 1,2 %A A050132 _Clark Kimberling_