A087739 a(1)=1; a(2)=2; for n > 2, a(n) satisfies a(S(n))=n and a(k)=n-1 for S(n-1) < k < S(n) where S(n) = a(1) + a(2) + ... + a(n).

1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18

Offset: 1

Author

Benoit Cloitre, Oct 01 2003

Keywords

• nonn
• changed

Examples

			a(a(1) + a(2) + a(3)) = 3 and a(1) + a(2) + a(3) = 5, hence a(5)=3. And since a(1) + a(2) < 4 < a(1) + a(2) + a(3) we have a(4) = 3 - 1 = 2.
		

Crossrefs

Cf. A001462.

Formula

Limit_{n->oo} a(n)*n/S(n) = phi = (1+sqrt(5))/2; a(n) is asymptotic to phi^(2-phi)*n^(phi-1) as the Golomb sequence A001462; more precisely A001462(n) - a(n) = 0 or 1.

For n > 2, a(n) = A001462(n-1).