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Numbers whose binary expansion contains group of at least two 1's followed by a nonempty group of 0's.
1

%I #9 Feb 20 2022 22:38:16

%S 6,12,14,24,28,30,48,56,60,62,96,112,120,124,126,192,224,240,248,252,

%T 254,384,448,480,496,504,508,510,768,896,960,992,1008,1016,1020,1022,

%U 1536,1792,1920,1984,2016,2032,2040,2044,2046,3072,3584,3840,3968,4032

%N Numbers whose binary expansion contains group of at least two 1's followed by a nonempty group of 0's.

%C All terms are even.

%H Michael S. Branicky, <a href="/A118586/b118586.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{n>=1} 1/a(n) = -1 + A065442. - _Amiram Eldar_, Feb 20 2022

%e 4080_10 = 111111110000_2.

%t Sort[Flatten[Table[Sum[2^k,{k,k1,k2}],{k1,1,10},{k2,k1+1,11}]]]

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o for d in count(3):

%o for i in range(2, d):

%o yield int("1"*i + "0"*(d-i), 2)

%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, Feb 20 2022

%Y Cf. A043569, A065442.

%K base,nonn

%O 1,1

%A _Zak Seidov_, May 07 2006