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

%I A354775 #12 Jun 27 2022 08:24:57
%S A354775 5,9,25,37,49,67,73,91,97,145,193,289,385,577,769,1153,1537,2305,3073,
%T A354775 4609,6145,9217,12289,18433,24577,36865,49153,73729,98305,147457,
%U A354775 196609,294913,393217,589825,786433,1179649,1572865,2359297,3145729,4718593,6291457
%N A354775 Indices where A354169 is the sum of two consecutive powers of 2.
%C A354775 A subsequence of A354798.
%C A354775 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 A354775 Rémy Sigrist, <a href="/A354775/a354775.txt">C++ program</a>
%o A354775 (C++) See Links section.
%o A354775 (Python)
%o A354775 from itertools import count, islice
%o A354775 from collections import deque
%o A354775 from functools import reduce
%o A354775 from operator import or_
%o A354775 def A354775_gen(): # generator of terms
%o A354775     aset, aqueue, b, f, i = {0,1,2}, deque([2]), 2, False, 2
%o A354775     while True:
%o A354775         for k in count(1):
%o A354775             m, j, j2, r, s = 0, 0, 1, b, k
%o A354775             while r > 0:
%o A354775                 r, q = divmod(r,2)
%o A354775                 if not q:
%o A354775                     s, y = divmod(s,2)
%o A354775                     m += y*j2
%o A354775                 j += 1
%o A354775                 j2 *= 2
%o A354775             if s > 0:
%o A354775                 m += s*2**b.bit_length()
%o A354775             if m not in aset:
%o A354775                 i += 1
%o A354775                 if '11' in (s := bin(m)[2:]) and s.count('1') == 2:
%o A354775                     yield i
%o A354775                 aset.add(m)
%o A354775                 aqueue.append(m)
%o A354775                 if f: aqueue.popleft()
%o A354775                 b = reduce(or_,aqueue)
%o A354775                 f = not f
%o A354775                 break
%o A354775 A354775_list = list(islice(A354775_gen(),15)) # _Chai Wah Wu_, Jun 27 2022
%Y A354775 Cf. A354169, A354680, A354767, A354798, A354773-A354774.
%K A354775 nonn
%O A354775 1,1
%A A354775 _N. J. A. Sloane_, Jun 26 2022
%E A354775 More terms from _Rémy Sigrist_, Jun 27 2022