cp's OEIS Frontend

A358139 Numbers k > 0 sorted by k/A000120(k) in increasing order. A000120 is the binary weight of k. If k/A000120(k) yields equal values, the smaller k will appear first.

%I A358139 #25 Nov 17 2022 14:12:15
%S A358139 1,3,2,7,5,6,11,15,4,13,9,14,10,23,12,31,19,27,21,29,22,30,8,25,17,26,
%T A358139 18,28,47,39,20,63,43,55,45,46,35,59,24,61,37,62,38,51,53,54,41,42,57,
%U A358139 58,44,60,79,95,16,49,33,50,34,52,87,71,36,127,91,111,93,56
%N A358139 Numbers k > 0 sorted by k/A000120(k) in increasing order. A000120 is the binary weight of k. If k/A000120(k) yields equal values, the smaller k will appear first.
%C A358139 A permutation of the positive integers.
%C A358139 This permutation satisfies a weak ordering: If b = a(c*d) and e = a(c) and f = a(d) then b > e and b > f with c,d > 1.
%H A358139 Thomas Scheuerle, <a href="/A358139/a358139.png">a(1..25000) as scatter plot</a>.
%H A358139 Thomas Scheuerle, <a href="/A358139/a358139_1.png">a(1..1000) as scatter plot colored by binary weight and a(n)/A000120(a(n)) plotted as blue line</a>.
%H A358139 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A358139 a(2^n) = 2^(n+1) - 1.
%F A358139 abs(a(n)-n) < n.
%o A358139 (PARI) f(x) = x/hammingweight(x);
%o A358139 cmpb(x, y) = my(hx=f(x), hy=f(y)); if (hx != hy, return(sign(hx-hy))); return(sign(x-y));
%o A358139 lista(nn) = Vec(vecsort([1..2*nn], cmpb, 1), nn); \\ _Michel Marcus_, Nov 05 2022
%Y A358139 Cf. A000120, A049445, A161764, A199238, A235602, A348416.
%K A358139 nonn,easy,base
%O A358139 1,2
%A A358139 _Thomas Scheuerle_, Oct 31 2022