A192086 - OEIS

%I #24 Aug 05 2024 10:59:50

%S 219,309,349,438,467,565,618,665,698,701,817,876,885,934,1130,1141,

%T 1143,1236,1291,1297,1299,1330,1396,1397,1402,1435,1629,1634,1659,

%U 1752,1755,1770,1771,1773,1868,1905,2155,2229,2260,2282,2286,2353,2401,2472,2582

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

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

%C This sequence is infinite, since if k is in the sequence then so is 2k. - _Charles R Greathouse IV_, Sep 27 2016

%H Nathaniel Johnston, <a href="/A192086/b192086.txt">Table of n, a(n) for n = 1..2500</a>

%e 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.

%p 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

%t Select[Range[2800],DigitCount[#^3,2,1]<DigitCount[#^2,2,1]&] (* _Harvey P. Dale_, Jun 30 2011 *)

%t Flatten@Position[Flatten@(Differences@DigitSum[#^2*{1, #}, 2] & /@Range@15000), _?(# < 0 &)] (* _Hans Rudolf Widmer_, Aug 05 2024 *)

%o (Magma) [ n: n in [0..2600] | &+Intseq(n^3,2) lt &+Intseq(n^2,2) ];  // _Bruno Berselli_, Jun 24 2011

%o (PARI) is(n)=hammingweight(n^3)<hammingweight(n^2) \\ _Charles R Greathouse IV_, Sep 27 2016

%Y Cf. A000120, A159918, A192085.

%K nonn,base

%O 1,1

%A _Carl R. White_, Jun 23 2011