

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
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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(7i)=a(8+i) for i=1,2,...,6, and a(22j)=a(23+j) for j=1..21.
Decimal expansion of 13801675776055042253380279/999000999000999000999000999.  Jianing Song, Apr 04 2021


LINKS

Table of n, a(n) for n=0..89.
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(n30).
a(n) = a(n3)  a(n6) + a(n9)  a(n12) + a(n15)  a(n18) + a(n21)  a(n24) + a(n27).
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

Cf. A000032, A000045, A001906, A130893.
Bisection of A003893.
Sequence in context: A073227 A016550 A238169 * A086245 A247392 A219995
Adjacent sequences: A341411 A341412 A341413 * A341415 A341416 A341417


KEYWORD

easy,nonn


AUTHOR

Jens Rasmussen, Feb 11 2021


STATUS

approved



