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

5, 9, 17, 23, 27, 29, 33, 39, 43, 45, 51, 53, 57, 65, 71, 75, 77, 83, 85, 89, 95, 99, 101, 105, 111, 113, 119, 123, 125, 129, 135, 139, 141, 147, 149, 153, 159, 163, 165, 169, 175, 177, 183, 187, 189, 195, 197, 201, 207, 209, 215, 219, 221, 225, 231, 235, 237

Offset

1,1

Links

Lei Zhou, Table of n, a(n) for n = 1..10000

Index entries for sequences related to binary expansion of n

Formula

a(2^n - floor(n/2)) = 4*2^n + 1, for all n >= 0. - Gheorghe Coserea, Oct 24 2016

Example

Binary expansions of odd integers in decimal and binary forms are as follows:
   1 ->     1, no;
   3 ->    11, no;
   5 ->   101, yes, so a(1)=5;
   7 ->   111, no;
   9 ->  1001, yes so a(2)=9;
  11 ->  1011, no;
  13 ->  1101, no;
  15 ->  1111, no;
  17 -> 10001, yes so a(3)=17.

Mathematica

BNDigits[m_Integer] :=
  Module[{n = m, d, t = {}},
   While[n > 0, d = Mod[n, 2]; PrependTo[t, d]; n = (n - d)/2]; t];
c = 1;
Table[While[c = c + 2; d = BNDigits[c]; ld = Length[d];
  c1 = Total[d]; ! (EvenQ[c1] && (c1 < ld))]; c, {n, 1, 57}]

Prog

(PARI) isok(n) = my(b=binary(n)); (n % 2) && (vecmin(b)==0) && !(vecsum(b) % 2); \\ Michel Marcus, Oct 21 2016
(PARI)
seq(N) = {
  my(bag = List(), cnt = 0, n = 1);
  while(cnt < N,
        if (hammingweight(n)%2 == 0 && hammingweight(n+1) > 1,
            listput(bag, n); cnt++);
        n += 2);
  return(Vec(bag));
};
seq(57)  \\ Gheorghe Coserea, Oct 25 2016

Crossrefs

Cf. A005408.

Intersection of A129771 and A062289.

Sequence in context: A095725 A005006 A369318 * A157970 A054278 A210978

Adjacent sequences: A276191 A276192 A276193 * A276195 A276196 A276197

Keyword

nonn,base

Author

Lei Zhou, Oct 20 2016

Status

approved