[seqfan] Re: relation of A019529 and A054040, partial sums of 1/sqrt(j)
Rainer Rosenthal
r.rosenthal at web.de
Sat Aug 29 18:13:44 CEST 2009
David Wilson wrote:
> Yes. Looks like A054040 is in error. Should be deaded and merged into
> A019529.
Right so.
A019529(n) = 1, 2, 3, 5, 7, ...
A054040(n) = 1, 3, 5, 7, ...
Let b(k) = 1 + 1/sqrt(2) + 1(sqrt(3) + ... + 1/sqrt(k)
and
a(n) = smallest k such that b(k) > n, i = 0,1,2,3,...
Sequence a(n) is what A054040 and A019529 are meant to be,
according to their definition.
k 1 2 3 4 5 6 7
-------------------------------------------------
b(k) 1.00 1.71 2.28 2.78 3.23 3.64 4.01
n=0: smallest k is a(0) = 1 since 1.00 > 0
n=1: smallest k is a(1) = 2 since 1.71 > 1
n=2: smallest k is a(2) = 3 since 2.28 > 2
n=3: smallest k is a(3) = 5 since 3.23 > 3
n=4: smallest k is a(4) = 7 since 4.01 > 4
Thus sequence a(n) starts with 1, 2, 3, 5, 7, which is what
A054040 fails to do.
Cheers,
Rainer
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