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Odd numbers with exactly 3 ones in binary expansion.
8

%I #19 Feb 14 2022 01:23:33

%S 7,11,13,19,21,25,35,37,41,49,67,69,73,81,97,131,133,137,145,161,193,

%T 259,261,265,273,289,321,385,515,517,521,529,545,577,641,769,1027,

%U 1029,1033,1041,1057,1089,1153,1281,1537,2051,2053,2057,2065,2081,2113,2177

%N Odd numbers with exactly 3 ones in binary expansion.

%H Amiram Eldar, <a href="/A084468/b084468.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert Baillie, <a href="http://arxiv.org/abs/0806.4410">Summing the curious series of Kempner and Irwin</a>, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.

%F a(n) = 2*A018900(n) + 1 = A005408(A018900(n)).

%F Sum_{n>=1} 1/a(n) = 0.714295772926319061998427422200268976390844375453066534198594764887682975019... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022

%t Flatten[Table[2^m + 2^n + 1, {m, 2, 11}, {n, m - 1}]] (* _Alonso del Arte_, Jul 08 2011 *)

%o (PARI) for(m=2, 9, for(n=1, m-1, print1(2^m+2^n+1", "))) \\ _Charles R Greathouse IV_, Oct 04 2011

%Y Intersection of A005408 and A014311.

%Y A084470(n) gives the position of a(n) in A084467(n).

%Y Cf. A018900.

%K nonn,base,easy

%O 1,1

%A _Antti Karttunen_, Jun 02 2003