[seqfan] Re: Palindome reciprocal sums

[M. F. Hasler]

Charles observes that applying Aitken's delta squared, "the value is singular".
More precisely, Lars' sequence has the first differences
[2.5821 E-9, 2.5822 E-9, 1.2911 E-9, 1.2911 E-9 ]
I think if this is not "suspicious", at least it is certainly not an accident.
The logical sequel would be (for 1st differences) :
 6.4555E-10,  6.4555E-10,  3.22775 E-10, 3.22775 E-10, 1.613875 E-10,
1.613875 E-10, 8.069375 E-11, 8.069375 E-11,...
which would yield, for the values :
a(60) = 2.37879570560475
a(61) =  2.3787957062503
a(62) = 2.378795706573075
a(63) = 2.37879570689585
a(64) = 2.3787957070572375
a(65) = 2.378795707218625
a(66) = 2.37879570729931875
a(67) = 2.3787957073800125

Maximilian

On Sat, Jun 21, 2014 at 11:22 AM, Lars Blomberg <lars.blomberg at visit.se> wrote:
> For summing to 55-59 binary digits I get
>
> 55    2.3787956972127
> 56    2.3787956997948
> 57    2.3787957023770
> 58    2.3787957036681
> 59    2.3787957049592
>
> /Lars Blomberg
>
> -----Ursprungligt meddelande----- From: Frank Adams-Watters Sent: Friday,
> June 20, 2014 11:18 PM To: seqfan at list.seqfan.eu Subject: [seqfan] Palindome
> reciprocal sums
> We have
> A118031, sum of reciprocals of decimal palindromes
> A118064 sum of reciprocals of decimal palindromic primes
> A194097 sum of reciprocals of binary palindromic primes
>
> But we don't have the one I would consider the most basic, the sum of the
> reciprocals of binary palindromes.