A031448 Numbers whose base-2 representation has one fewer 0's than 1's.

1, 5, 6, 19, 21, 22, 25, 26, 28, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 271, 279, 283, 285, 286, 295, 299, 301, 302, 307, 309, 310, 313, 314, 316, 327, 331, 333, 334, 339, 341, 342

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

A037861(a(n)) = -1. - Reinhard Zumkeller, Mar 31 2015

The viabin numbers of the integer partitions in which the number of parts is equal to the largest part (for the definition of viabin number see comment in A290253). For example, 99 is in the sequence because it is the viabin number of the integer partition [4,2,2,2]. - Emeric Deutsch, Aug 29 2017

Examples

			99 is in the sequence because its binary form is 1100011. - _Emeric Deutsch_, Aug 29 2017
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088, A023416, A000120, A031444, subsequence of A089648.

Programs

Haskell

a031448 n = a031448_list !! (n-1)
a031448_list = filter ((== -1) . a037861) [1..]
-- Reinhard Zumkeller, Mar 31 2015

Maple

vitopart := proc (n) local L, i, j, N, p, t: N := 2*n; L := ListTools:-Reverse(convert(N, base, 2)): j := 0: for i to nops(L) do if L[i] = 0 then j := j+1: p[j] := numboccur(L[1 .. i], 1) end if end do: sort([seq(p[t], t = 1 .. j)], `>=`) end proc: A := {}; for m to 500 do if nops(vitopart(m)) = max(vitopart(m)) then A := `union`(A, {m}) else  end if end do: A; # program is based on my comment; the command vitopart(n) yields the integer partition having viabin number n. - Emeric Deutsch, Aug 29 2017

Mathematica

Select[Range[400],DigitCount[#,2,1]==DigitCount[#,2,0]+1&] (* Harvey P. Dale, May 24 2019 *)