A348416 -id:A348416 - 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.

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

Thomas Scheuerle, Oct 31 2022

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.

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

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

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

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

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

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.

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