%I #7 May 02 2024 17:34:06

%S 0,1,3,5,11,27,71,119,140,158,198,218,441,537,538,868,1092,2128,2294,

%T 2343,2811,2911,3849,4003,4655,5079,5279,5920,6269,6603,10181,10574,

%U 12801,12803,15563,15784,16054,16253,17127,18257,20187,21934,34633,49209,76791,78938

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

%C These are the k-values ​​of the upper 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 differences are given in A372100.

%H Hugo Pfoertner, <a href="/A372099/b372099.txt">Table of n, a(n) for n = 1..96</a>

%H Hugo Pfoertner, <a href="/A372099/a372099.png">Illustration of scatter band bounded by lower and upper records</a>, up to exponents k=8.5*10^6.

%o (PARI) a372099(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 a372099(80000)

%Y Cf. A000120, A000244, A011754, A070939, A078839, A372097, A372098, A372100.

%K nonn

%O 1,3

%A _Hugo Pfoertner_, Apr 25 2024