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

Author

Carl R. White, Jun 23 2011

Keywords

• nonn
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000120, A159918, A192085.

Programs

Magma

[ n: n in [0..2600] | &+Intseq(n^3,2) lt &+Intseq(n^2,2) ];  // Bruno Berselli, Jun 24 2011

Maple

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

Mathematica

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

PARI

is(n)=hammingweight(n^3)Charles R Greathouse IV, Sep 27 2016