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A371916 Zeroless analog of tetranacci numbers.

%I A371916 #23 May 05 2024 09:50:33
%S A371916 1,1,1,1,4,7,13,25,49,94,181,349,673,1297,25,2344,4339,85,6793,13561,
%T A371916 24778,45217,9349,9295,88639,1525,1888,11347,13399,28159,54793,17698,
%U A371916 11449,11299,95239,135685,253672,495895,98491,983743,183181,176131,1441546,278461,279319,2175457
%N A371916 Zeroless analog of tetranacci numbers.
%C A371916 It is not known whether this sequence cycles, but it is conjectured to cycle just like A243063 and A371911 (have periods of 912 and 300056874, respectively) because the expected growth factor in the number of digits of successive terms is 0.9.
%C A371916 It's been computationally verified that if the sequence does cycle, then s+p > 10^10, where s and p are the starting index and period of the cycle, respectively.
%F A371916 a(n) = Zr(a(n-1)+a(n-2)+a(n-3)+a(n-4)), where the function Zr(k) removes zero digits from k.
%e A371916 a(14) = Zr(a(13)+a(12)+a(11)+a(10)) = Zr(1297+673+349+181) = Zr(2500) = 25.
%t A371916 a[0]=a[1]=a[2]=a[3]=1; a[n_]:=FromDigits[DeleteCases[IntegerDigits[a[n-1]+a[n-2]+a[n-3]+a[n-4]], 0]]; Array[a, 46, 0] (* _Stefano Spezia_, Apr 12 2024 *)
%o A371916 (Python)
%o A371916 def a(n):
%o A371916     a, b, c, d = 1, 1, 1, 1
%o A371916     for _ in range(n):
%o A371916         a, b, c, d = b, c, d, int(str(a+b+c+d).replace('0', ''))
%o A371916     return a
%o A371916 (Python) # faster for initial segment of sequence
%o A371916 from itertools import islice
%o A371916 def agen(): # generator of terms
%o A371916     a, b, c, d = 1, 1, 1, 1
%o A371916     while True:
%o A371916         yield a
%o A371916         a, b, c, d = b, c, d, int(str(a+b+c+d).replace("0", ""))
%o A371916 print(list(islice(agen(), 45))) # _Michael S. Branicky_, Apr 13 2024
%Y A371916 Cf. A000045, A000213, A000288, A004719, A242350, A243657, A243658, A243063.
%K A371916 nonn,base
%O A371916 0,5
%A A371916 _Bryle Morga_, Apr 12 2024