A372099 Exponents k where A000120(3^k) - A070939(3^k)/2 reaches a new maximum.

0, 1, 3, 5, 11, 27, 71, 119, 140, 158, 198, 218, 441, 537, 538, 868, 1092, 2128, 2294, 2343, 2811, 2911, 3849, 4003, 4655, 5079, 5279, 5920, 6269, 6603, 10181, 10574, 12801, 12803, 15563, 15784, 16054, 16253, 17127, 18257, 20187, 21934, 34633, 49209, 76791, 78938

Offset

1,3

Comments

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.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..96

Hugo Pfoertner, Illustration of scatter band bounded by lower and upper records, up to exponents k=8.5*10^6.

Prog

(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))};
a372099(80000)

Crossrefs

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

Sequence in context: A292855 A374572 A265941 * A333629 A308545 A368808

Adjacent sequences: A372096 A372097 A372098 * A372100 A372101 A372102

Keyword

nonn

Author

Hugo Pfoertner, Apr 25 2024

Status

approved