A087739 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..79.

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) = round(phi^(2-phi)*(n-1)^(1-phi)) where phi = (1+sqrt(5))/2;

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

EXAMPLE

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.

Sequence in context: A176844 A085182 A211339 * A375814 A127763 A057367

Adjacent sequences: A087736 A087737 A087738 * A087740 A087741 A087742

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Oct 01 2003

STATUS

approved