[math-fun] Sum of last ten digits

[Hans Havermann]

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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