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A341414
a(n) = (Fibonacci(n)*Lucas(n)) mod 10.
1
0, 1, 3, 8, 1, 5, 4, 7, 7, 4, 5, 1, 8, 3, 1, 0, 9, 7, 2, 9, 5, 6, 3, 3, 6, 5, 9, 2, 7, 9, 0, 1, 3, 8, 1, 5, 4, 7, 7, 4, 5, 1, 8, 3, 1, 0, 9, 7, 2, 9, 5, 6, 3, 3, 6, 5, 9, 2, 7, 9, 0, 1, 3, 8, 1, 5, 4, 7, 7, 4, 5, 1, 8, 3, 1, 0, 9, 7, 2, 9, 5, 6, 3, 3, 6, 5, 9, 2, 7, 9
OFFSET
0,3
COMMENTS
Fibonacci starting with 0,1 and Lucas starting with 2,1.
Blocks of 30 numbers with 10 even and 20 uneven numbers.
Symmetric as a(7-i)=a(8+i) for i=1,2,...,6, and a(22-j)=a(23+j) for j=1..21.
Decimal expansion of 13801675776055042253380279/999000999000999000999000999. - Jianing Song, Apr 04 2021
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,-1,0,0,1,0,0,-1,0,0,1,0,0,-1,0,0,1,0,0,-1,0,0,1).
FORMULA
a(n) = (Fibonacci(n)*Lucas(n)) mod 10 = Fibonacci(2*n) mod 10 using Binet's formula for Fibonacci and corresponding formula for Lucas.
a(n) = a(n-30).
a(n) = a(n-3) - a(n-6) + a(n-9) - a(n-12) + a(n-15) - a(n-18) + a(n-21) - a(n-24) + a(n-27).
a(n) = A003893(2*n).
EXAMPLE
For n=5: a(5) = (Fibonacci(5)*Lucas(5)) mod 10 = (5*11) mod 10 = 55 mod 10 = 5.
MATHEMATICA
Table[Mod[Fibonacci@n*LucasL@n, 10], {n, 0, 100}] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
PROG
(PARI) a(n) = fibonacci(2*(n%30)) % 10 \\ Jianing Song, Apr 04 2021
CROSSREFS
Bisection of A003893.
Sequence in context: A073227 A016550 A238169 * A086245 A247392 A219995
KEYWORD
easy,nonn
AUTHOR
Jens Rasmussen, Feb 11 2021
STATUS
approved