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Numbers with binary weight (A000120) <= 3.
2

%I #17 Feb 14 2022 01:23:29

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,24,25,26,28,

%T 32,33,34,35,36,37,38,40,41,42,44,48,49,50,52,56,64,65,66,67,68,69,70,

%U 72,73,74,76,80,81,82,84,88,96,97,98,100,104,112,128,129,130,131,132,133,134,136

%N Numbers with binary weight (A000120) <= 3.

%C There are O(log^4 x) members of this sequence up to x. - _Charles R Greathouse IV_, Mar 29 2013

%H Charles R Greathouse IV, <a href="/A095736/b095736.txt">Table of n, a(n) for n = 1..5000</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 Sum_{n>=2} 1/a(n) = 4.957591106549526542379494338911534917897082748621184321529665450307117309571... (calculated using Baillie's irwinSums.m, see Links). - _Amiram Eldar_, Feb 14 2022

%t Select[Range[0,150],DigitCount[#,2,1]<4&] (* _Harvey P. Dale_, Apr 11 2012 *)

%o (PARI) is(n)=hammingweight(n)<4 \\ _Charles R Greathouse IV_, Mar 29 2013

%Y Cf. A000079, A000120, A048645, A018900, A084468, A014311, A001969, A000069.

%K nonn,base,easy

%O 1,3

%A _N. J. A. Sloane_, Jun 23 2009