A192086 Numbers n such that the binary weight (A000120) of n^3 is less than the binary weight of n^2.

219, 309, 349, 438, 467, 565, 618, 665, 698, 701, 817, 876, 885, 934, 1130, 1141, 1143, 1236, 1291, 1297, 1299, 1330, 1396, 1397, 1402, 1435, 1629, 1634, 1659, 1752, 1755, 1770, 1771, 1773, 1868, 1905, 2155, 2229, 2260, 2282, 2286, 2353, 2401, 2472, 2582

Offset

1,1

Comments

Numbers n such that A192085(n) < A159918(n).

This sequence is infinite, since if k is in the sequence then so is 2k. - Charles R Greathouse IV, Sep 27 2016

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..2500

Example

219^2 decimal = 1011101101011001 binary, and 219^3 decimal = 101000000100010100100011; Since the cube has fewer ones in its binary expansion than the square (eight versus ten), 219 is in the list.

Maple

A192086 := proc(n) return `if`(add(b, b=convert(n^3, base, 2))<add(b, b=convert(n^2, base, 2)), n, NULL): end: seq(A192086(n), n=0..3000); # Nathaniel Johnston, Jun 23 2011

Mathematica

Select[Range[2800], DigitCount[#^3, 2, 1]<DigitCount[#^2, 2, 1]&] (* Harvey P. Dale, Jun 30 2011 *)
Flatten@Position[Flatten@(Differences@DigitSum[#^2*{1, #}, 2] & /@Range@15000), _?(# < 0 &)] (* Hans Rudolf Widmer, Aug 05 2024 *)

Prog

(Magma) [ n: n in [0..2600] | &+Intseq(n^3, 2) lt &+Intseq(n^2, 2) ];  // Bruno Berselli, Jun 24 2011
(PARI) is(n)=hammingweight(n^3)<hammingweight(n^2) \\ Charles R Greathouse IV, Sep 27 2016

Crossrefs

Cf. A000120, A159918, A192085.

Sequence in context: A025406 A025404 A361343 * A256815 A179580 A043435

Adjacent sequences: A192083 A192084 A192085 * A192087 A192088 A192089

Keyword

nonn,base

Author

Carl R. White, Jun 23 2011

Status

approved