A329653 Describe n in binary, convert to decimal: write in base 10 the binary number concat(c0,0,c1,1) where c0, c1 is the number of '0's and '1's in n, all written in binary.

9, 3, 11, 5, 19, 21, 21, 7, 27, 37, 37, 23, 37, 23, 23, 9, 35, 53, 53, 39, 53, 39, 39, 41, 53, 39, 39, 41, 39, 41, 41, 11, 43, 69, 69, 55, 69, 55, 55, 73, 69, 55, 55, 73, 55, 73, 73, 43, 69, 55, 55, 73, 55, 73, 73, 43, 55, 73, 73, 43, 73, 43, 43, 13, 51, 85, 85, 71, 85

Offset

0,1

Links

Table of n, a(n) for n=0..68.

Formula

a(n+1) = a(n) if n == 1 (mod 4), n > 1.

Example

In the binary expansion of n = 0, we have one '0', zero '1's => 1001[2] = 9[10] = a(0).
In the binary expansion of n = 1, we have zero '0's, one '1' => 0011 = 3[10] = a(1).
In the binary expansion of n = 2 = 10[2], we have one '0', one '1' => 1011[2] = 11[10] = a(2).
In the binary expansion of n = 3 = 11[2], we have zero '0's, two (= 10[2]) '1's => a(3) = 00101[2] = 5[10].

Prog

(PARI) apply( {d(a, b=2)=fromdigits(concat([binary(logint(a+!a, 2)+1-a=hammingweight(a)), 0, if(a, binary(a)), 1]), b)}, [0..99]) \\ 2n optional arg: base in which the string of bits is to be read - i.e., b=10: write it in binary, b=2: convert to decimal!

Crossrefs

Cf. A329652 (a(n) written in binary), A010062.

Sequence in context: A363872 A166203 A248312 * A170874 A309791 A103935

Adjacent sequences: A329650 A329651 A329652 * A329654 A329655 A329656

Keyword

nonn,base

Author

M. F. Hasler, Nov 18 2019

Status

approved