[seqfan] RE : Recurring Digital Invariant

[Eric Angelini]

I wrote:
 
> First fixed points:
> S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, ...

... obviously not: 14 ends up on 370, which is a known fixed point -- 14 is not a fixed point by itself...
Best,
E.
 

 
________________________________

De: seqfan-bounces at list.seqfan.eu de la part de Eric Angelini
Date: mar. 17/02/2009 19:10
À: Sequence Fanatics Discussion list
Objet : [seqfan] Recurring Digital Invariant




Hello SeqFans,
http://mathworld.wolfram.com/RecurringDigitalInvariant.html <http://mathworld.wolfram.com/RecurringDigitalInvariant.html> 
... what if k = "length of the considered integer"?

(k = 2 for the integer 14, for instance)

Starting with said 14:

 14 -> 1^2 + 4^2 = 17
 17 -> 1^2 + 7^2 = 50
 50 -> 5^2 + 0^2 = 25
 25 -> 2^2 + 5^2 = 29
 29 -> 2^2 + 9^2 = 85
 85 -> 8^2 + 5^2 = 89
 89 -> 8^2 + 9^2 = 145
145 -> 1^3 + 4^3 + 5^3 = 190
190 -> 1^3 + 9^3 + 0^3 = 730
730 -> 7^3 + 3^3 + 0^3 = 370
370 -> 3^3 + 7^3 + 0^3 = 370 (fixed point)

First fixed points:
S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 14, ...
Any more?

Best,
É.






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