This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A192086 #24 Aug 05 2024 10:59:50
%S A192086 219,309,349,438,467,565,618,665,698,701,817,876,885,934,1130,1141,
%T A192086 1143,1236,1291,1297,1299,1330,1396,1397,1402,1435,1629,1634,1659,
%U A192086 1752,1755,1770,1771,1773,1868,1905,2155,2229,2260,2282,2286,2353,2401,2472,2582
%N A192086 Numbers n such that the binary weight (A000120) of n^3 is less than the binary weight of n^2.
%C A192086 Numbers n such that A192085(n) < A159918(n).
%C A192086 This sequence is infinite, since if k is in the sequence then so is 2k. - _Charles R Greathouse IV_, Sep 27 2016
%H A192086 Nathaniel Johnston, <a href="/A192086/b192086.txt">Table of n, a(n) for n = 1..2500</a>
%e A192086 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 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 A192086 Select[Range[2800],DigitCount[#^3,2,1]<DigitCount[#^2,2,1]&] (* _Harvey P. Dale_, Jun 30 2011 *)
%t A192086 Flatten@Position[Flatten@(Differences@DigitSum[#^2*{1, #}, 2] & /@Range@15000), _?(# < 0 &)] (* _Hans Rudolf Widmer_, Aug 05 2024 *)
%o A192086 (Magma) [ n: n in [0..2600] | &+Intseq(n^3,2) lt &+Intseq(n^2,2) ]; // _Bruno Berselli_, Jun 24 2011
%o A192086 (PARI) is(n)=hammingweight(n^3)<hammingweight(n^2) \\ _Charles R Greathouse IV_, Sep 27 2016
%Y A192086 Cf. A000120, A159918, A192085.
%K A192086 nonn,base
%O A192086 1,1
%A A192086 _Carl R. White_, Jun 23 2011