A087275 Write n in binary: 1ab..yz, then a(n) = 1b..yz + ... + 1yz + 1z + 1.

0, 1, 1, 3, 4, 3, 4, 7, 9, 9, 11, 7, 9, 9, 11, 15, 18, 19, 22, 19, 22, 23, 26, 15, 18, 19, 22, 19, 22, 23, 26, 31, 35, 37, 41, 39, 43, 45, 49, 39, 43, 45, 49, 47, 51, 53, 57, 31, 35, 37, 41, 39, 43, 45, 49, 39, 43, 45, 49, 47, 51, 53, 57, 63, 68, 71, 76

Offset

1,4

Comments

a(n) = A087276(n) - n.

Links

Table of n, a(n) for n=1..67.

Formula

a(1) = 0, a(2n) = 2*a(n) + 1, a(2n+1) = 2*a(n) + floor(log_2(n)) + 1.

Prog

(PARI) a(n)=local(v, s, l); v=binary(n); l=length(v); s=0; for(k=2, l, s=s+2^(l-k)+sum(m=k+1, l, v[m]*2^(l-m))); s

Crossrefs

Cf. A005187, A059893, A059894.

Sequence in context: A178152 A006984 A361458 * A265305 A072942 A025267

Adjacent sequences: A087272 A087273 A087274 * A087276 A087277 A087278

Keyword

nonn,easy

Author

Ralf Stephan, Aug 27 2003

Status

approved