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

0,4

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).

Links

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

Example

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

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:

Crossrefs

Cf. A050430, A215469.

Sequence in context: A057432 A361942 A302295 * A284266 A317988 A038568

Adjacent sequences: A215464 A215465 A215466 * A215468 A215469 A215470

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 11 2012

Status

approved