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A130893
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Lucas numbers (beginning with 1) mod 10.
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8
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1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, 4
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OFFSET
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0,2
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COMMENTS
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Period 12: repeat [1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2].
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..10000
Maarten Bullynck, L’histoire de l’informatique et l’histoire des mathématiques : rencontres, opportunités et écueils, Images des Mathématiques, CNRS, 2015 (in French).
Johann Heinrich Lambert, Anlage zur Architectonic, oder Theorie des Einfachen und des Ersten in der philosophischen und mathematischen Erkenntniß, 1771.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
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FORMULA
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a(n) = (a(n-2) + a(n-1)) mod 10, with a(0) = 1, a(1) = 3.
a(n) = A000204(n+1) mod 10 = A000032(n+1) mod 10. - Joerg Arndt, Sep 17 2013
a(n) = f(5(n-1)+2) mod 10, where f(n) is the n-th Fibonacci number (A000045). - Joseph P. Shoulak, Sep 15 2013
From G. C. Greubel, Feb 08 2016: (Start)
a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11).
a(n+12) = a(n). (End)
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EXAMPLE
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1 + 3 = 4 = 4 mod 10, then a(3) = 4.
3 + 4 = 7 = 7 mod 10, then a(4) = 7.
4 + 7 = 11 = 1 mod 10, then a(5) = 1.
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MATHEMATICA
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Nest[Append[#, Mod[Total[Take[#, -2]], 10]] &, {1, 3}, 110] (* Harvey P. Dale, Apr 05 2011 *)
t = {1, 3}; Do[AppendTo[t, Mod[t[[-1]] + t[[-2]], 10]], {99}]; t (* T. D. Noe, Sep 16 2013 *)
Mod[LucasL[Range[100]], 10] (* Alonso del Arte, Sep 30 2015 *)
LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1}, {1, 3, 4, 7,
1, 8, 9, 7, 6, 3, 9}, 100] (* G. C. Greubel, Feb 08 2016 *)
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PROG
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(Ruby)
def truncM10(n)
..a = 1
..b = 3
..n.times do
....a, b = (b % 10), ((a + b) % 10)
..end
..return b
end
# Joseph P. Shoulak, Sep 15 2013
(PARI) a(n) = (fibonacci(n+1)+fibonacci(n-1)) % 10;
vector(100, n, a(n)) \\ Altug Alkan, Sep 30 2015
(MAGMA) [Lucas(n) mod 10: n in [1..100]]; // Vincenzo Librandi, Oct 01 2015
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CROSSREFS
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Cf. A000032, A003983, A111958.
Sequence in context: A173014 A322017 A093087 * A072079 A116073 A166043
Adjacent sequences: A130890 A130891 A130892 * A130894 A130895 A130896
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KEYWORD
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easy,nonn,base
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 22 2007
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EXTENSIONS
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Corrected and extended by Harvey P. Dale, Apr 05 2011
New name from Joerg Arndt, Sep 17 2013
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STATUS
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approved
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