A329652 Describe n in binary: concat(c0,0,c1,1) where c0, c1 is the number of '0's and '1's in n, all written in binary.

1001, 11, 1011, 101, 10011, 10101, 10101, 111, 11011, 100101, 100101, 10111, 100101, 10111, 10111, 1001, 100011, 110101, 110101, 100111, 110101, 100111, 100111, 101001, 110101, 100111, 100111, 101001, 100111, 101001, 101001, 1011, 101011, 1000101, 1000101, 110111, 1000101, 110111

Offset

0,1

Links

Table of n, a(n) for n=0..37.

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 => a(0) = 1001.
In the binary expansion of n = 1, we have zero '0's, one '1' => a(0) = 0011 (leading 0's not showing up in DATA).
In the binary expansion of n = 2 = 10[2], we have one '0', one '1' => a(2) = 1011.
In the binary expansion of n = 3 = 11[2], we have zero '0's, two (= 10[2]) '1's => a(2) = 00101 (leading 0's not showing up in DATA).
5 = 101[2] => a(5) = 1 0 10 1.
6 = 110[2] => a(6) = 1 0 10 1: illustration of the formula.

Prog

(PARI) apply( {A329652(a, b=10)=fromdigits(concat([binary(logint(a+!a, 2)+1-a=hammingweight(a)), 0, if(a, binary(a)), 1]), b)}, [0..40]) \\ 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. A329653 (convert a(n) from binary to decimal), A010062.

Sequence in context: A283014 A283058 A283080 * A077493 A290663 A290544

Adjacent sequences: A329649 A329650 A329651 * A329653 A329654 A329655

Keyword

nonn,base

Author

M. F. Hasler, Nov 18 2019

Status

approved