[seqfan] Re: Recursions in decimal expansions

[Heinz, Alois]

A216407 lacks a precise definition.  Any idea how to compute A216407(10)?

In the first example a(1) = 49 I cannot see the coefficient 1 in
1/49 = 0.020408163265306122448...

Why is 98 not in the sequence? We have
1/98 = 0.0102040816326530612244897959...
1/98 = sum( 2^i * 10^(-2*i-2), i=0..infinity)
I see 1, 2, 4, 8, 16, 32, ... "and then it gets scrambled".

Why is 96 not in the sequence?
1/96 = 0.01041666666666666666666...
1/96 = sum(4^i*10^(-2*i-2), i=0..infinity)
I see 1, 4, 16, ... "and then it gets scrambled".

How early is "scrambling" allowed?

Alois

Am 24.09.2012 17:50, schrieb Charles Greathouse:
> A216407, "Positive integers n such that the initial part of the
> decimal expansion of  1/n reveals a recursive sequence", is an
> interesting idea for a sequence. I'm bringing this up to SeqFan
> because I don't know how to make it precise. In fact I'm concerned
> that, when made precise, it will turn out to be a duplicate of
> A000027.
>
> The examples from the sequence explain themselves pretty well:
>
> a(1)=49 is in the sequence, because 1/49 = 0.020408163265306122448...
> shows the coefficients 1, 2, 4, 8, 16, 32, ... and then it gets
> scrambled.
> a(2)=97  is in the sequence, because 1/97 = 0.01030927835051546...
> shows the coefficients 1, 3, 9, 27, ... and then it gets scrambled.
> a(3)=9899 is in the sequence, because 1/9899 =
> 0.0001010203050813213455904636832003232649762602283058... shows the
> first Fibonacci numbers  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,... and
> then it gets scrambled.
>
> This is an exhaustive list at present.
> [ ... ]