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A261694
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a(n) = Fibonacci(n) mod 21.
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1
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0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1, 0, 1, 1, 2, 3, 5, 8, 13, 0, 13
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OFFSET
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0,4
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COMMENTS
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Sequence is periodic with Pisano period 16; Pisano number 21 in the sequence A001175. The only other sequence with Pisano period 16 is that of A105870 which is the Fibonacci sequence mod 7. This is Pisano number 7.
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LINKS
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FORMULA
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G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 13*x^8 + 13*x^9 + 5*x^10 + 18*x^11 + 2*x^12 + 20*x^13 + x^14)/(1-x^16).
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MATHEMATICA
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Table[Mod[Fibonacci[n], 21], {n, 0, 100}]
PadRight[{}, 120, {0, 1, 1, 2, 3, 5, 8, 13, 0, 13, 13, 5, 18, 2, 20, 1}] (* Harvey P. Dale, May 16 2020 *)
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PROG
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(PARI) a(n) = fibonacci(n)%21; \\ Altug Alkan, Nov 19 2015
(Python)
for _ in range(10**3):
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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