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

%I A031448 #18 Jul 04 2021 13:47:47
%S A031448 1,5,6,19,21,22,25,26,28,71,75,77,78,83,85,86,89,90,92,99,101,102,105,
%T A031448 106,108,113,114,116,120,271,279,283,285,286,295,299,301,302,307,309,
%U A031448 310,313,314,316,327,331,333,334,339,341,342
%N A031448 Numbers whose base-2 representation has one fewer 0's than 1's.
%C A031448 A037861(a(n)) = -1. - _Reinhard Zumkeller_, Mar 31 2015
%C A031448 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
%H A031448 Reinhard Zumkeller, <a href="/A031448/b031448.txt">Table of n, a(n) for n = 1..10000</a>
%H A031448 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A031448 99 is in the sequence because its binary form is 1100011. - _Emeric Deutsch_, Aug 29 2017
%p A031448 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
%t A031448 Select[Range[400],DigitCount[#,2,1]==DigitCount[#,2,0]+1&] (* _Harvey P. Dale_, May 24 2019 *)
%o A031448 (Haskell)
%o A031448 a031448 n = a031448_list !! (n-1)
%o A031448 a031448_list = filter ((== -1) . a037861) [1..]
%o A031448 -- _Reinhard Zumkeller_, Mar 31 2015
%Y A031448 Cf. A007088, A023416, A000120, A031444, subsequence of A089648.
%K A031448 nonn,base
%O A031448 1,2
%A A031448 _Clark Kimberling_