A372097 Exponents k where A000120(3^k) - A070939(3^k)/2 reaches a new minimum.

0, 2, 4, 7, 16, 24, 40, 49, 53, 102, 104, 126, 174, 226, 379, 768, 831, 832, 1439, 1452, 1914, 2291, 2731, 3000, 3363, 3472, 5608, 5883, 6725, 6787, 7438, 8786, 10280, 11948, 12190, 13135, 15170, 15645, 22407, 26232, 27099, 32773, 33085, 40189, 40523, 48068, 51187

Offset: 1

Author

Hugo Pfoertner, Apr 25 2024

Keywords

• nonn

Comments

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.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..99
• Hugo Pfoertner, Illustration of scatter band bounded by lower and upper records, up to exponents k=8*10^6.

Crossrefs

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

Programs

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))};
a372097(60000)