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

Author

N. J. A. Sloane, Jun 26 2022

Keywords

• nonn

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

• Rémy Sigrist, C++ program

Crossrefs

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

Programs

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

Extensions

More terms from Rémy Sigrist, Jun 27 2022