A354775 Indices where A354169 is the sum of two consecutive powers of 2.

5, 9, 25, 37, 49, 67, 73, 91, 97, 145, 193, 289, 385, 577, 769, 1153, 1537, 2305, 3073, 4609, 6145, 9217, 12289, 18433, 24577, 36865, 49153, 73729, 98305, 147457, 196609, 294913, 393217, 589825, 786433, 1179649, 1572865, 2359297, 3145729, 4718593, 6291457

Offset

1,1

Comments

A subsequence of A354798.

The first differences begin 4, 16, 12, 12, 18, 6, 18, 6, 48, 48, 96, 96, 192, 192, 384, 384, 768, 768, 1536, ..., which suggests that from the 9th term on, the differences have g.f. 48*(1+x)/(1-2*x^2), with an analogous conjecture for the sequence itself.

Links

Table of n, a(n) for n=1..41.

Rémy Sigrist, C++ program

Prog

(C++) See Links section.
(Python)
from itertools import count, islice
from collections import deque
from functools import reduce
from operator import or_
def A354775_gen(): # generator of terms
    aset, aqueue, b, f, i = {0, 1, 2}, deque([2]), 2, False, 2
    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:
                i += 1
                if '11' in (s := bin(m)[2:]) and s.count('1') == 2:
                    yield i
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                b = reduce(or_, aqueue)
                f = not f
                break
A354775_list = list(islice(A354775_gen(), 15)) # Chai Wah Wu, Jun 27 2022

Crossrefs

Cf. A354169, A354680, A354767, A354798, A354773-A354774.

Sequence in context: A273746 A234277 A269918 * A273827 A024825 A147074

Adjacent sequences: A354772 A354773 A354774 * A354776 A354777 A354778

Keyword

nonn

Author

N. J. A. Sloane, Jun 26 2022

Extensions

More terms from Rémy Sigrist, Jun 27 2022

Status

approved