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

1,2

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A063445 A257331 A240400 * A290254 A163772 A056509

Adjacent sequences: A031445 A031446 A031447 * A031449 A031450 A031451

Keyword

nonn,base

Author

Clark Kimberling

Status

approved