A095736 Numbers with binary weight (A000120) <= 3.

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, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 52, 56, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 80, 81, 82, 84, 88, 96, 97, 98, 100, 104, 112, 128, 129, 130, 131, 132, 133, 134, 136

Offset: 1

Author

N. J. A. Sloane, Jun 23 2009

Keywords

• nonn
• base
• easy

Comments

There are O(log^4 x) members of this sequence up to x. - Charles R Greathouse IV, Mar 29 2013

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..5000
• Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015. See p. 18 for Mathematica code irwinSums.m.

Crossrefs

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

Programs

Mathematica

Select[Range[0,150],DigitCount[#,2,1]<4&] (* Harvey P. Dale, Apr 11 2012 *)

PARI

is(n)=hammingweight(n)<4 \\ Charles R Greathouse IV, Mar 29 2013

Formula

Sum_{n>=2} 1/a(n) = 4.957591106549526542379494338911534917897082748621184321529665450307117309571... (calculated using Baillie's irwinSums.m, see Links). - Amiram Eldar, Feb 14 2022