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A130893 Lucas numbers (beginning with 1) mod 10. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Period 12: repeat [1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2].
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
FORMULA
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)
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A173014 A322017 A093087 * A072079 A116073 A166043
KEYWORD
easy,nonn,base
AUTHOR
Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 22 2007
EXTENSIONS
Corrected and extended by Harvey P. Dale, Apr 05 2011
New name from Joerg Arndt, Sep 17 2013
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)