cp's OEIS Frontend

Conjecture: if we write a(m) = 2^m + d then d < 2*m for m > 2. The reason for this conjecture: the Hamming weight of a number is smaller than its binary logarithm. If we assume in A357961 a random distribution of Hamming weights with values < log_2(k) for A357961(k), then we may expect for each dyadic interval an increase in displacement by the half of the intervals exponent. If we assume instead of randomness a stronger repeating of any Hamming weight, we would even reduce the gained displacement by this. - Thomas Scheuerle, Oct 24 2022