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A003893
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a(n) = Fibonacci(n) mod 10.
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33
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0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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All blocks of 60 successive terms contain 20 even and 40 odd numbers. - Reinhard Zumkeller, Apr 09 2005
These are the analogs of the Fibonacci numbers in carryless arithmetic mod 10.
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REFERENCES
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G. Marsaglia, The mathematics of random number generators, pp. 73-90 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1).
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FORMULA
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Periodic with period 60 = A001175(10).
a(n) = (a(n-1) + a(n-2)) mod 10 for n > 1, a(0) = 0, a(1) = 1.
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MAPLE
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with(combinat, fibonacci); A003893 := proc(n) fibonacci(n) mod 10; end;
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MATHEMATICA
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Table[Mod[Fibonacci[n], 10], {n, 0, 99}] (* Alonso del Arte, Jul 29 2013 *)
Table[IntegerDigits[Fibonacci[n]][[-1]], {n, 0, 99}] (* Alonso del Arte, Jul 29 2013 *)
NumberDigit[Fibonacci[Range[0, 120]], 0] (* Requires Mathematica version 12 or later *) (* Harvey P. Dale, Jul 05 2021 *)
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PROG
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(Haskell)
a003893 n = a003893_list !! n
a003893_list = 0 : 1 : zipWith (\u v -> (u + v) `mod` 10)
(tail a003893_list) a003893_list
(Python)
for _ in range(10**3):
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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