sum of 1/A007504(n)

[Brendan McKay]

Assuming that the magnitude of the tail of the sum is something of
order 1/(n*log(n)) after n terms, I guess the final value is about
1.0234763237 or 1.0234763238. However, this type of convergence
acceleration of slowly converging sums has a habit of producing
illusions, so this guess may well be way off.  It would be
better to make a theoretical estimate of the tail and add that
to the partial sums.

Brendan.


* Simon Plouffe <simon.plouffe at gmail.com> [070516 07:44]:
> 
> Hello, here are the latest results.
> 
> 1.0234763205449071151695629254011 after reaching
> the 30244000'th prime.
> 
> Here is a trace of the last computation
> 
>  Sum                                  term             index
> =============================================================
> 1.0234763205433771485177329655746, 8493160443506957, 30231000
> 1.0234763205434948863081814357548, 8493738372115593, 30232000
> 1.0234763205436126160876758199314, 8494316321695723, 30233000
> 1.0234763205437303378570190511747, 8494894291396737, 30234000
> 1.0234763205438480516170236077605, 8495472281427875, 30235000
> 1.0234763205439657573684938130720, 8496050292177521, 30236000
> 1.0234763205440834551122280724106, 8496628324121853, 30237000
> 1.0234763205442011448490288997553, 8497206376389379, 30238000
> 1.0234763205443188265797046941143, 8497784448902379, 30239000
> 1.0234763205444365003050644095177, 8498362541614343, 30240000
> 1.0234763205445541660259204510602, 8498940654066589, 30241000
> 1.0234763205446718237430861024454, 8499518786938911, 30242000
> 1.0234763205447894734573634207349, 8500096940380361, 30243000
> 1.0234763205449071151695629254011, 8500675113418419, 30244000
> 
> again : close to 1/2+Pi/6 but considering that the last
> term is of the order of 1/8500675113418419 and the
> diff. with the supposed value is ony 1/8166 approx.
> 
> I don't see where all this would converge to it.
> 
> Simon Plouffe
> 
> 
>