A089399 a(n) satisfies: 2^a(n)+1 = sum(k=1,n, A089398(k)*2^(k-1)) for n>2, with a(1)=a(2)=0.

0, 0, 3, 4, 5, 6, 8, 9, 10, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 51, 52, 53, 54, 55, 57, 58, 59, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 69, 70, 71, 72, 73

Offset

1,3

Comments

A089398(n) = n-th column sum of binary digits of k*2^(k-1), where summation is over all k>=1, without carrying from columns sums that may exceed 2.

Links

Table of n, a(n) for n=1..72.

Example

a(7)=8 since 2^8+1=257=(1)+(0)2+(2)2^2+(1)2^3+(1)2^4+(1)2^5+(3)2^6,
and A089398 begins: {1,0,2,1,1,1,3,2,2,0,3,2,2,2,4,3,3,1,...}.

Crossrefs

Cf. A089398.

Sequence in context: A112768 A298420 A197354 * A003619 A377721 A216846

Adjacent sequences: A089396 A089397 A089398 * A089400 A089401 A089402

Keyword

nonn

Author

Paul D. Hanna, Oct 30 2003

Status

approved