[seqfan] Re: Palindome reciprocal sums
Joseph S. Myers
jsm at polyomino.org.uk
Mon Jun 23 12:13:13 CEST 2014
On Sun, 22 Jun 2014, M. F. Hasler wrote:
> 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.
Well, you expect the sum of reciprocals of 2n+1-digit palindromes to be
about the same as the sum of reciprocals of 2n-digit palindromes (in base
b, there are b times as many of them, which balances out the palindromes
being about b times bigger), while the sum of reciprocals of 2n+2-digit
palindromes should be about 1/b times the sum for 2n+1 digits (the same
number of them, and again they are about b times bigger).
--
Joseph S. Myers
jsm at polyomino.org.uk
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