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A112395 Next term is the sum of the previous 10 digits in the sequence.

%I A112395 #16 Oct 04 2024 08:51:55
%S A112395 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,
%T A112395 50,44,40,37,37,37,42,40,40,34,31,25,26,30,29,33,35,36,37,44,41,40,36,
%U A112395 36,35,35,38,45,45,45,46,48,49,53,52,50,45,42,35,35,36,40,35,37,39,43,41
%N A112395 Next term is the sum of the previous 10 digits in the sequence.
%C A112395 Digits, not terms!
%C A112395 There are only 10^10 possibilities for the last 10 digits, so the sequence must eventually cycle.
%C A112395 Cycles at n(19) = 44 and the loop has 312 terms. - _Hans Havermann_
%C A112395 Terms computed by Gilles Sadowski.
%H A112395 Michael S. Branicky, <a href="/A112395/b112395.txt">Table of n, a(n) for n = 1..331</a> (through first loop)
%e A112395 0 + 0 + 1 + 1 + 2 + 4 + 8 + 1 + 6 = 23
%t A112395 a[1] = a[2] = a[3] = a[4] = a[5] = a[6] = a[7] = a[8] = a[9] = 0; a[10] = 1; a[n_] := a[n] = Plus @@ Take[ Flatten@Table[IntegerDigits[a[i]], {i, n - 10, n - 1}], -10]; Array[a, 74] (* _Robert G. Wilson v_, Dec 09 2005 *)
%o A112395 (Python)
%o A112395 from itertools import islice
%o A112395 def agen(): # generator of terms
%o A112395     last10 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
%o A112395     print(last10[:0])
%o A112395     yield from last10
%o A112395     while True:
%o A112395         an = sum(last10)
%o A112395         yield an
%o A112395         d = list(map(int, str(an)))
%o A112395         last10 = last10[-max(10-len(d), 0):] + d[-min(len(d), 10):]
%o A112395 print(list(islice(agen(), 74))) # _Michael S. Branicky_, Oct 03 2024
%K A112395 base,easy,nonn
%O A112395 1,12
%A A112395 _Eric Angelini_, Dec 05 2005