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.

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, 18, 28, 47, 39, 20, 63, 43, 55, 45, 46, 35, 59, 24, 61, 37, 62, 38, 51, 53, 54, 41, 42, 57, 58, 44, 60, 79, 95, 16, 49, 33, 50, 34, 52, 87, 71, 36, 127, 91, 111, 93, 56

Offset

1,2

Comments

A permutation of the positive integers.

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.

Links

Table of n, a(n) for n=1..68.

Thomas Scheuerle, a(1..25000) as scatter plot.

Thomas Scheuerle, a(1..1000) as scatter plot colored by binary weight and a(n)/A000120(a(n)) plotted as blue line.

Index entries for sequences that are permutations of the natural numbers

Formula

a(2^n) = 2^(n+1) - 1.

abs(a(n)-n) < n.

Prog

(PARI) f(x) = x/hammingweight(x);
cmpb(x, y) = my(hx=f(x), hy=f(y)); if (hx != hy, return(sign(hx-hy))); return(sign(x-y));
lista(nn) = Vec(vecsort([1..2*nn], cmpb, 1), nn); \\ Michel Marcus, Nov 05 2022

Crossrefs

Cf. A000120, A049445, A161764, A199238, A235602, A348416.

Sequence in context: A059894 A307544 A126314 * A358654 A200714 A086702

Adjacent sequences: A358136 A358137 A358138 * A358140 A358141 A358142

Keyword

nonn,easy,base

Author

Thomas Scheuerle, Oct 31 2022

Status

approved