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

1,2

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.

Prog

(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)

Crossrefs

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

Sequence in context: A303749 A239390 A338647 * A361334 A026731 A026764

Adjacent sequences: A372094 A372095 A372096 * A372098 A372099 A372100

Keyword

nonn

Author

Hugo Pfoertner, Apr 25 2024

Status

approved