cp's OEIS Frontend

A276194 Odd numbers whose binary representation contains an even number of 1's and at least one 0.

%I A276194 #58 Jan 13 2019 03:09:29
%S A276194 5,9,17,23,27,29,33,39,43,45,51,53,57,65,71,75,77,83,85,89,95,99,101,
%T A276194 105,111,113,119,123,125,129,135,139,141,147,149,153,159,163,165,169,
%U A276194 175,177,183,187,189,195,197,201,207,209,215,219,221,225,231,235,237
%N A276194 Odd numbers whose binary representation contains an even number of 1's and at least one 0.
%H A276194 Lei Zhou, <a href="/A276194/b276194.txt">Table of n, a(n) for n = 1..10000</a>
%H A276194 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A276194 a(2^n - floor(n/2)) = 4*2^n + 1, for all n >= 0. - _Gheorghe Coserea_, Oct 24 2016
%e A276194 Binary expansions of odd integers in decimal and binary forms are as follows:
%e A276194    1 ->     1, no;
%e A276194    3 ->    11, no;
%e A276194    5 ->   101, yes, so a(1)=5;
%e A276194    7 ->   111, no;
%e A276194    9 ->  1001, yes so a(2)=9;
%e A276194   11 ->  1011, no;
%e A276194   13 ->  1101, no;
%e A276194   15 ->  1111, no;
%e A276194   17 -> 10001, yes so a(3)=17.
%t A276194 BNDigits[m_Integer] :=
%t A276194   Module[{n = m, d, t = {}},
%t A276194    While[n > 0, d = Mod[n, 2]; PrependTo[t, d]; n = (n - d)/2]; t];
%t A276194 c = 1;
%t A276194 Table[While[c = c + 2; d = BNDigits[c]; ld = Length[d];
%t A276194   c1 = Total[d]; ! (EvenQ[c1] && (c1 < ld))]; c, {n, 1, 57}]
%o A276194 (PARI) isok(n) = my(b=binary(n)); (n % 2) && (vecmin(b)==0) && !(vecsum(b) % 2); \\ _Michel Marcus_, Oct 21 2016
%o A276194 (PARI)
%o A276194 seq(N) = {
%o A276194   my(bag = List(), cnt = 0, n = 1);
%o A276194   while(cnt < N,
%o A276194         if (hammingweight(n)%2 == 0 && hammingweight(n+1) > 1,
%o A276194             listput(bag, n); cnt++);
%o A276194         n += 2);
%o A276194   return(Vec(bag));
%o A276194 };
%o A276194 seq(57)  \\ _Gheorghe Coserea_, Oct 25 2016
%Y A276194 Cf. A005408.
%Y A276194 Intersection of A129771 and A062289.
%K A276194 nonn,base
%O A276194 1,1
%A A276194 _Lei Zhou_, Oct 20 2016