A357993 a(n) is the unique k such that A357961(k) = 2^n.

1, 2, 9, 8, 17, 34, 64, 129, 252, 515, 1026, 2044, 4091, 8184, 16375, 32758, 65525, 131060, 262131, 524279, 1048566, 2097167, 4194322, 8388590, 16777203, 33554450, 67108877, 134217712, 268435473, 536870929, 1073741807, 2147483622, 4294967278, 8589934615

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..33.

Rémy Sigrist, PARI program

Formula

Empirically: a(n) ~ 2^n.

Example

A357961(1026) = 1024 = 2^10, so a(10) = 1026.

Prog

(PARI) See Links section.

Crossrefs

Cf. A357961.

Sequence in context: A069815 A215025 A162954 * A129194 A300780 A272347

Adjacent sequences: A357990 A357991 A357992 * A357994 A357995 A357996

Keyword

nonn,base

Author

Rémy Sigrist, Oct 23 2022

Status

approved