A082968 a(n)=sum(k=1,n, k mod sum(i=0,k-1,1-t(i))) where t(i)=A010060(i) is the Thue-Morse sequence.

0, 0, 0, 0, 1, 1, 4, 4, 5, 5, 10, 10, 16, 16, 17, 17, 18, 18, 27, 27, 37, 37, 38, 38, 50, 50, 51, 51, 52, 52, 67, 67, 68, 68, 85, 85, 103, 103, 104, 104, 124, 124, 125, 125, 126, 126, 149, 149, 173, 173, 174, 174, 175, 175, 202, 202, 203, 203, 232, 232, 262, 262, 263, 263

Offset

1,7

Links

Table of n, a(n) for n=1..64.

Formula

Despite the definition, a(n) has an unexpectedly simple asymptotic behavior h: a(n)=(n/4)^2 +O(n) and more precisely it appears that : (n/4)^2-n/8 <= a(n) < (n/4)^2+n/2 with equality (on left side) for infinitely many values of n.

Prog

(PARI) a(n)=sum(k=1, n, k%sum(i=0, k-1, 1-subst(Pol(binary(i)), x, 1)%2))

Crossrefs

Sequence in context: A257291 A152465 A357414 * A136013 A232172 A114884

Adjacent sequences: A082965 A082966 A082967 * A082969 A082970 A082971

Keyword

nonn

Author

Benoit Cloitre, May 27 2003

Status

approved