A274069 a(n) is the concatenation of a(n-1) and the Hamming distance between a(n-1) and its reverse (i.e., the minimum number of bitflips needed to make them identical). Sequence written in binary.

1, 10, 1010, 1010100, 101010010, 101010010110, 101010010110100, 101010010110100100, 1010100101101001001000, 10101001011010010010001110, 101010010110100100100011101100, 10101001011010010010001110110010100, 101010010110100100100011101100101001100, 10101001011010010010001110110010100110011000, 10101001011010010010001110110010100110011000100000

Offset: 1

Author

Meir-Simchah Panzer, Jun 09 2016

Keywords

• nonn
• base
• easy

Examples

			Let a'(n) be the reverse of a(n). E.g., if a(n) = 10100, then a'(n) = 00101. Let hamm(b,c) denote the Hamming distance between b and c. Let concat designate concatenation of arguments.
a(1):=1.
a(2) is the concatenation of a(1) and hamm(a(1),a'(1)). a'(1) = 1. So hamm(a(1),a'(1)) = hamm('1','1') = 0. So a(2) = concat('1','0') = 10.
a(3) is the concatenation of a(2) and hamm(a(2),a'(2)). hamm(a(2),a'(2)) = hamm('10','01') = 2 or 10 in base 2. So a(3) = concat('10','10') = 1010.
a(4) is the concatenation of a(3) and hamm(a(3),a'(3)). hamm(a(3),a'(3)) = hamm('1010','0101') = 4 or 100 in base 2. So a(3) = concat('1010','100') = 10100.
		

Crossrefs

Cf. A144078.

Programs

Maple

A274069aux := proc(n)
    option remember;
    if n = 1 then
        [1];
    else
        d := procname(n-1) ;
        dreve := ListTools[Reverse](d) ;
        ham := 0 ;
        for i from 1 to nops(d) do
            if op(i,d) <> op(i,dreve) then
                ham := ham+1 ;
            end if;
        end do:
        if ham = 0 then
            [op(d),0] ;
        else
            ListTools[Reverse](convert(ham,base,2)) ;
            [op(d),op(%) ] ;
        end if ;
    end if;
end proc:
A274069 := proc(n)
    digcatL(A274069aux(n)) ;
end proc:
seq(A274069(n),n=1..30) ; # R. J. Mathar, May 08 2019

Extensions

Edited by Meir-Simchah Panzer, Jun 12 2018

More terms from R. J. Mathar, May 08 2019.