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A071532
a(n) = (-1) * Sum_{k=1..n} (-1)^floor((3/2)^k).
4
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
1,4
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.....
FORMULA
a(n) = (-1) * Sum_{i=1..n} (-1)^A002379(i).
MATHEMATICA
a[0] = 0; a[n_] := a[n] = a[n - 1] - (-1)^Floor[(3/2)^n]; Table[ a[n], {n, 0, 95}]
PROG
(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))
CROSSREFS
Sequence in context: A017861 A094700 A073635 * A102730 A165597 A269757
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 20 2002
EXTENSIONS
Edited by Ralf Stephan, Sep 01 2004
STATUS
approved