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A372097
Exponents k where A000120(3^k) - A070939(3^k)/2 reaches a new minimum.
4
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, 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)
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Apr 25 2024
STATUS
approved