A071532 a(n) = (-1) * Sum_{k=1..n} (-1)^floor((3/2)^k).

1, 0, 1, 2, 3, 4, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 10, 9, 8, 9, 8, 9, 8, 7, 8, 7, 8, 9, 10, 11, 10, 9, 10, 9, 8, 7, 8, 7, 6, 7, 8, 7, 8, 7, 6, 5, 6, 7, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 10, 11, 10, 11, 10, 9, 10, 9, 10, 9, 8, 7, 6, 5, 6, 7, 6, 7, 6, 5, 4, 5, 6, 5, 4, 5, 4, 3

Offset: 1

Author

Benoit Cloitre, Jun 20 2002

Keywords

• easy
• nonn

Comments

Let b(n) denote the number of k with 0<=k<=n such that floor((3/2)^k) = A002379(k) is even; then a(n) = n-2*b(n).

Equivalently: let c(n) denote the number of k, 0<=k<=n, such that floor((3/2)^k) = A002379(k) is odd, then a(n) = 2*c(n)-n.

Is a(n)>0? For n large enough does a(n)>sqrt(n) always hold?

Conjecture: asymptotically, a(n) ~ C * Log(n)^2 with C = 1.4.....

Links

• Robert G. Wilson v, Graph of first 100000 terms

Crossrefs

Cf. A002379, A072418.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = a[n - 1] - (-1)^Floor[(3/2)^n]; Table[ a[n], {n, 0, 95}]

PARI

a(n)=-sum(i=1, n, sign((-1)^floor((3/2)^i)))

PARI

a(n)=n-2*sum(k=0,n,if(floor((3/2)^k)%2,0,1))

Formula

a(n) = (-1) * Sum_{i=1..n} (-1)^A002379(i).

Extensions

Edited by Ralf Stephan, Sep 01 2004