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Odd numbers k such that hammingweight(k^2) < hammingweight(k).
1

%I #19 Mar 14 2022 08:46:28

%S 23,47,95,111,191,223,367,383,415,447,479,727,767,831,887,895,959,

%T 1451,1471,1503,1535,1663,1727,1775,1783,1791,1855,1917,1919,1983,

%U 2527,2911,2943,2991,3071,3327,3455,3549,3551,3567,3575,3583,3695,3711,3837,3839,3967,3999,5793,5823,5855,5883,5885,5887,5949,5951,5983,5993,5999

%N Odd numbers k such that hammingweight(k^2) < hammingweight(k).

%C Odd terms in A094694.

%H David A. Corneth, <a href="/A352291/b352291.txt">Table of n, a(n) for n = 1..10000</a>

%p select(t -> convert(convert(t^2,base,2),`+`) < convert(convert(t,base,2),`+`), [seq(i,i=1..10^4,2)]); # _Robert Israel_, Mar 13 2022

%t Select[Range[1, 6000, 2], Greater @@ DigitCount[{#, #^2}, 2, 1] &] (* _Amiram Eldar_, Mar 11 2022 *)

%o (PARI) forstep(n=1,10^4,2,if(hammingweight(n^2)<hammingweight(n),print1(n,", ")));

%o (Python)

%o def ok(n): return n%2 == 1 and bin(n).count('1') > bin(n**2).count('1')

%o print([k for k in range(6000) if ok(k)]) # _Michael S. Branicky_, Mar 11 2022

%Y Cf. A000120, A094694.

%K nonn,base

%O 1,1

%A _Joerg Arndt_, Mar 11 2022