# [seqfan] RE : 8/5 Sequence

kohmoto zbi74583.boat at orange.zero.jp
Fri Jun 22 03:12:29 CEST 2012

```    Thanks for Maximilian's explanation.
I understood that A082010 is the map of 8/5 sequence.
I had thought that it is the orbit of 0.

Neil
I think both your sequence  are correct.

I found three 8/5 sequences which have long periods.

S.1.
a(n)=[A*a(n-1)+B]/2^n
Where [M] is Integer part of M.
2^n is the highest two power dividing [A*a(n-1)+B]

a(0)=7, A=1.6, B=1.00000001
Period=5082

S.2.
a(0)=7, A=1.6, B=1.00000002
Period=1664

S.3.
a(0)=7, A=1.6, B=1.00000003
Period=107365

The case of B=1.0, it is probably unlimited.
Because Don Reble computed the 2000000th term and it has 46000 digits.
In this mail  8/5 sequence is represented as a K-Sequence.
So periods become much shorter.

I computed these three sequence using a program written in UBASIC.
This language makes a mistake sometimes.
Could anyone confirm these results?
Could anyone also confirm Reble's result?
I wonder if A152199 is limited or not.

Yasutoshi

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