%I #7 May 02 2024 17:33:57

%S 0,2,4,7,16,24,40,49,53,102,104,126,174,226,379,768,831,832,1439,1452,

%T 1914,2291,2731,3000,3363,3472,5608,5883,6725,6787,7438,8786,10280,

%U 11948,12190,13135,15170,15645,22407,26232,27099,32773,33085,40189,40523,48068,51187

%N Exponents k where A000120(3^k) - A070939(3^k)/2 reaches a new minimum.

%C These are the k-values ​​of the lower envelope of the scatter band of the deviation of the binary weight of 3^k from half the length of the corresponding binary number. The corresponding negated differences are given in A372098.

%H Hugo Pfoertner, <a href="/A372097/b372097.txt">Table of n, a(n) for n = 1..99</a>

%H Hugo Pfoertner, <a href="/A372097/a372097.png">Illustration of scatter band bounded by lower and upper records</a>, up to exponents k=8*10^6.

%o (PARI) a372097(upto) = {my (dm=-oo); for (k=0, upto, my (p=3^k, h=hammingweight(p), b=#binary(p)/2,d=b-h); if (d>dm, print1(k,", "); dm=d))};

%o a372097(60000)

%Y Cf. A000120, A000244, A011754, A070939, A078839, A372098, A372099, A372100.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Apr 25 2024