[math-fun] Sum of last ten digits

[Alexandre Wajnberg]

Dear Neil, Hans, Éric and Seqfans


It seems the shortest loop of Éric Angelini's < sum of last ten digits >
sequence is found [in the sequence beginning with a(10)=9] at term a(17)=45
and by a lenght of 1 term:
 
0 0 0 0 0 0 0 0 0 9 9 18 27 36 45 54 45 45 45 45 45 45 45 45 45

It should be interesting to taste the eight other (beginning with 2, 3 ...8)

Best!

Alexandre



De : Hans Havermann <pxp at rogers.com>
Date : Wed, 7 Dec 2005 11:42:44 -0500
À : <seqfan at ext.jussieu.fr>
Cc : "N. J. A. Sloane" <njas at research.att.com>
Objet : Re: [math-fun] Sum of last ten digits

On Dec 6, 2005, at 11:47 PM, N. J. A. Sloane wrote:

> 
> %S A112402 0,0,0,0,0,0,0,0,0,1,1,2,4
> %N A112402 Next term is the sum of the last 10 digits in the sequence.
> %C A112402 Digits, not terms!
> %C A112402 There are only 10^10 possibilities for the last 10 digits, so the
> sequence must eventually cycle.
>  

In fact, terms 19-23 (44, 40, 37, 42, 38) are repeated by terms 331-335
already.

Here are 335 terms:

{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 23, 28, 37, 44, 40, 37, 42,
38, 39, 43, 46, 46, 50, 44, 40, 37, 37, 37, 42, 40, 40, 34, 31, 25, 26, 30,
29, 33, 35, 36, 37, 44, 41, 40, 36, 36, 35, 35, 38, 45, 45, 45, 46, 48, 49,
53, 52, 50, 45, 42, 35, 35, 36, 40, 35, 37, 39, 43, 41, 42, 40, 34, 29, 33,
34, 35, 39, 44, 41, 40, 37, 39, 39, 43, 45, 50, 45, 42, 36, 38, 40, 39, 42,
42, 39, 40, 40, 32, 31, 29, 28, 34, 37, 42, 44, 41, 36, 38, 39, 45, 46, 51,
48, 49, 50, 46, 46, 50, 43, 37, 42, 38, 39, 46, 49, 52, 53, 50, 43, 40, 31,
28, 30, 28, 31, 31, 31, 25, 29, 30, 29, 36, 41, 39, 40, 41, 35, 34, 36, 33,
35, 38, 41, 39, 42, 42, 40, 33, 34, 29, 34, 35, 39, 45, 47, 47, 51, 49, 50,
46, 45, 43, 44, 39, 46, 46, 47, 51, 49, 50, 45, 44, 41, 40, 31, 30, 24, 22,
21, 20, 18, 24, 24, 26, 31, 33, 30, 27, 30, 25, 28, 32, 34, 32, 34, 34, 31,
30, 26, 29, 33, 32, 33, 36, 37, 36, 39, 46, 50, 46, 46, 47, 46, 46, 51, 47,
48, 49, 52, 49, 56, 56, 55, 52, 52, 46, 45, 43, 40, 37, 40, 34, 32, 30, 29,
30, 29, 33, 34, 38, 38, 46, 45, 48, 53, 50, 44, 42, 39, 39, 43, 45, 46, 50,
43, 38, 42, 39, 41, 41, 39, 40, 38, 37, 42, 43, 38, 45, 43, 40, 38, 42, 37,
38, 42, 44, 41, 40, 34, 30, 27, 28, 33, 35, 36, 42, 39, 41, 40, 36, 36, 39,
39, 46, 52, 50, 46, 44, 40, 34, 34, 36, 35, 35, 39, 44, 45, 45, 46, 48, 48,
52, 50, 46, 46, 44, 40, 37, 42, 38}


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