A215467 Length of longest palindromic prefix of (n base 2).

1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 3, 2, 2, 3, 4, 1, 5, 4, 4, 3, 5, 3, 3, 2, 2, 2, 5, 3, 3, 4, 5, 1, 6, 5, 5, 4, 4, 4, 4, 3, 3, 5, 5, 3, 6, 3, 3, 2, 2, 2, 6, 2, 2, 5, 5, 3, 3, 3, 3, 4, 4, 5, 6, 1, 7, 6, 6, 5, 5, 5, 5, 4, 7, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 5, 7, 5, 5, 3, 3, 6

Offset: 0

Author

N. J. A. Sloane, Aug 11 2012

Keywords

• nonn
• base

Comments

Since the binary expansion of n always begins with a 1, a final 0 can't affect the result, so a(2n) = a(n).

Examples

			...
4 = 100 -> 1
5 = 101 -> 3
6 = 110 -> 2
7 = 111 -> 3
8 = 1000 -> 1
9 = 1001 -> 4
...
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A050430, A215469.

Programs

Maple

rev := proc(lis)
    local t1,n,i;
    t1:=[]; n:=nops(lis);
    for i from 1 to n do t1:=[op(t1),lis[n+1-i]]; end do;
    return t1;
end proc;
isPal := proc(L)
    local d ;
    for d from 1 to nops(L)/2 do
        if op(d, L) <> op(-d, L) then
            return false;
        end if;
    end do:
    return true;
end proc:
A215467L := proc(L)
    local a, c;
    a := 1 ;
    for c from 2 to nops(L) do
        if isPal( [op(1..c, L)] ) then
            a := c ;
        end if;
    end do:
    return a;
end proc:
A215467 := proc(n)
    if n <= 1 then 1;
    else rev(convert(n, base, 2)) ;
        A215467L(%) ;
    end if;
end proc: