A354757 a(n) = Sum_{k = ceiling(n/2)..n-1} A354169(k).

0, 0, 1, 2, 6, 12, 15, 27, 59, 115, 127, 252, 508, 1004, 1021, 2013, 2047, 4031, 8127, 16307, 16375, 32631, 32767, 65279, 130815, 261375, 262143, 524270, 1048558, 2096110, 2097135, 4194253, 4194271, 8386527, 8388607, 16773119, 33550335, 67096575, 67108863

Offset: 0

Author

Rémy Sigrist, Jun 06 2022

Keywords

• nonn
• base

Comments

The 1's in the binary expansion of a(n) are forbidden in that of A354169(n). In other words, a(n) AND A354169(n) = 0 (where AND denotes the bitwise AND operator).

Examples

			a(5) = A354169(3) + A354169(4) = 4 + 8 = 12.
a(7) = A354169(4) + A354169(5) + A354169(6) = 8 + 3 + 16 = 27.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..4800
• Rémy Sigrist, Binary plot of a(n) (blue pixels) and A354169(n) (red pixels) for n=0..1000
• Rémy Sigrist, PARI program

Crossrefs

Cf. A354169, A354758.

A354780 is a bisection.

Programs

PARI

See Links section.

Python

from itertools import count, islice
from collections import deque
from functools import reduce
from operator import or_
def A354757_gen(): # generator of terms
    aset, aqueue, b, f = {0,1,2}, deque([2]), 2, False
    yield from (0,0,1)
    while True:
        for k in count(1):
            m, j, j2, r, s = 0, 0, 1, b, k
            while r > 0:
                r, q = divmod(r,2)
                if not q:
                    s, y = divmod(s,2)
                    m += y*j2
                j += 1
                j2 *= 2
            if s > 0:
                m += s*2**b.bit_length()
            if m not in aset:
                yield sum(aqueue)
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                b = reduce(or_,aqueue)
                f = not f
                break
A354757_list = list(islice(A354757_gen(),40)) # Chai Wah Wu, Jun 06 2022