A175453 a(1)=1. a(n) = sum a(k), where k, taken over the runs (of both 0's and 1's) in binary n, equals the length of each run.

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

Offset

1,2

Links

Jason Kimberley, Table of n, a(n) for n = 1..5000

Example

23 in binary is 10111. There is a run of one 1, followed by a run of one 0, followed finally by a run of three 1's. So, a(23) = a(1)+a(1)+a(3) = 1+1+2 = 4.

Prog

(Magma)
runs := function(s)
    r := []; c := 1;
    for i in [1..#s-1] do
        if s[i] eq s[i+1]
        then c +:= 1;
        else Append(~r, c); c := 1;
        end if;
    end for;
    Append(~r, c);
    return r;
end function;
A175453 := func<n|n eq 1 select 1 else
    &+[$$(k):k in runs(b)]where b is IntegerToSequence(n, 2)>;
// Jason Kimberley, Feb 11 2013

Crossrefs

Cf. A101211.

Sequence in context: A238268 A194883 A328404 * A014499 A055778 A348772

Adjacent sequences: A175450 A175451 A175452 * A175454 A175455 A175456

Keyword

base,nonn,easy

Author

Leroy Quet, May 16 2010

Extensions

Extended by Jason Kimberley, Feb 11 2013

Status

approved