A354775 - OEIS

%I #12 Jun 27 2022 08:24:57

%S 5,9,25,37,49,67,73,91,97,145,193,289,385,577,769,1153,1537,2305,3073,

%T 4609,6145,9217,12289,18433,24577,36865,49153,73729,98305,147457,

%U 196609,294913,393217,589825,786433,1179649,1572865,2359297,3145729,4718593,6291457

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

%C A subsequence of A354798.

%C 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.

%H Rémy Sigrist, <a href="/A354775/a354775.txt">C++ program</a>

%o (C++) See Links section.

%o (Python)

%o from itertools import count, islice

%o from collections import deque

%o from functools import reduce

%o from operator import or_

%o def A354775_gen(): # generator of terms

%o     aset, aqueue, b, f, i = {0,1,2}, deque([2]), 2, False, 2

%o     while True:

%o         for k in count(1):

%o             m, j, j2, r, s = 0, 0, 1, b, k

%o             while r > 0:

%o                 r, q = divmod(r,2)

%o                 if not q:

%o                     s, y = divmod(s,2)

%o                     m += y*j2

%o                 j += 1

%o                 j2 *= 2

%o             if s > 0:

%o                 m += s*2**b.bit_length()

%o             if m not in aset:

%o                 i += 1

%o                 if '11' in (s := bin(m)[2:]) and s.count('1') == 2:

%o                     yield i

%o                 aset.add(m)

%o                 aqueue.append(m)

%o                 if f: aqueue.popleft()

%o                 b = reduce(or_,aqueue)

%o                 f = not f

%o                 break

%o A354775_list = list(islice(A354775_gen(),15)) # _Chai Wah Wu_, Jun 27 2022

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 26 2022

%E More terms from _Rémy Sigrist_, Jun 27 2022