A356385 First differences of A353654 which is numbers with the same number of trailing 0 bits as other 0 bits.

2, 4, 3, 5, 7, 4, 5, 5, 10, 8, 4, 5, 13, 8, 10, 6, 10, 8, 4, 5, 9, 20, 16, 8, 10, 14, 8, 10, 6, 10, 8, 4, 5, 25, 16, 20, 12, 20, 16, 8, 10, 10, 20, 16, 8, 10, 14, 8, 10, 6, 10, 8, 4, 5, 17, 40, 32, 16, 20, 28, 16, 20, 12, 20, 16, 8, 10, 26, 16, 20, 12, 20, 16

Offset: 1

Author

Mikhail Kurkov, Aug 05 2022

Keywords

• nonn
• base

Crossrefs

Cf. A000045, A353654.

Programs

Mathematica

Differences @ Join[{1}, Select[Range[2, 1000], IntegerExponent[#, 2] == Floor[Log2[# - 1]] - DigitCount[# - 1, 2, 1] &]] (* Amiram Eldar, Sep 21 2022 *)

PARI

isok(k) = if (k==1, 1, (logint(k-1, 2)-hammingweight(k-1) == valuation(k, 2))); \\ A353654
lista(nn) = my(v=select(isok, [1..nn])); vector(#v-1, k, v[k+1] - v[k]); \\ Michel Marcus, Sep 21 2022
(Python 3.10+)
from itertools import pairwise, count, islice
def A356385_gen(): # generator of terms
    return map(lambda x:x[1]-x[0],pairwise(filter(lambda n:(~n & n-1).bit_length()<<1 == n.bit_length()-n.bit_count(),count(1))))
A356385_list = list(islice(A356385_gen(),30)) # Chai Wah Wu, Oct 14 2022

Formula

a(n) = A353654(n+1) - A353654(n) for n > 0.

a(A000045(n)-1) = 5 for n > 4.