request for help in clarifying definition of sequence

[Joshua Zucker]

I don't know much about zeta functions, but my limited understanding
of the explanation below is that the new sequence is supposed to be
the complement of A002410 .  I think he's implying that this sequence
is finite because the zeros of zeta get common enough that for some N,
every integer > N is in A002410, and thus no terms > N are in A120401.
 But I don't know enough about zeta to say whether that makes sense or
not.

--Joshua Zucker


On 9/16/06, N. J. A. Sloane <njas at research.att.com> wrote:
>
> Dear Seqfans,
>
> At present there is this entry:
>
> %I A120401
> %S A120401 0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,26,27,28,29,
> %T A120401 31,33,34,35,36,38,39,41,42,44,45,46,47,50,51,53,54,55,57,58,61,62,63,
> %U A120401 64,66,68
> %N A120401 Consider the zeros of the Riemann zeta function. Sequence gives the decimal part values which are nonzero.
> %D A120401 http://www.dtc.umn.edu/~odlyzko/zeta_tables/zeros1
> %e A120401 The first zero is 14.13472.. so 0,1,2,3,4,5,6,7,8,9,10,11,12,13 are part of the sequence
> %e A120401 The second zero is 21.02203.. so 15,16,17,18,19,20 are in the sequence too
> %e A120401 The third zero is 25.0108.. so 22,23,24, etc.
> %K A120401 fini,nonn,uned,obsc
> %O A120401 0,3
> %A A120401 Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Jul 02 2006
>
> I asked the author for more information.
>
> Dear Jorge,
> could you give a better definition of this sequence?
> I find it very confusing.
>
> and you might explain how it related to A002410!
>
> best
>
> Neil
>
> ----
>
>
> He said:
>
> ok  A002410  it the nearest integer to the imaginary part.
>
>   but imagine that there is a sequence that the integer part
>   is the integer part of the imaginary part of zeta. (not the nearet one)
>   I mean like (ceil function).
>
>   now A120401 is suppose to be the inverse of that function
>   so the numbers are fini. because when zero imaginary parts
>   become bigger they become all integer. so there must exist
>   a minimum number of integer numbers that are not associated
>   with any zero....  maybe I can finish the sequence by myself,
>   but I think it's big...  maybe a few hundred numbers. but it's fini.
>   because the zeta zeros become close
>
>
>
> ---
>
> I am still confused.  Could someone help and edit this sequence?
>
> Thanks
>
> Neil
>
>