OFFSET
1,1
COMMENTS
This is the length of the cycle for final n decimal digits in Lucas numbers (A000032).
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Lucas Number.
Index entries for linear recurrences with constant coefficients, signature (10).
FORMULA
a(n) = 3*10^(n-1) for n>2; a(1)=12, a(2)=60.
a(n) = lcm(3*2^(n-1),4*5^(n-1)). In particular, for n>=3, a(n) = 3*10^(n-1). - Max Alekseyev, May 17 2006
From Elmo R. Oliveira, Mar 28 2026: (Start)
G.f.: 12*x*(1 - 5*x - 25*x^2)/(1 - 10*x).
E.g.f.: (3/10)*(exp(10*x) - 1) + 3*x*(3 + 5*x).
a(n) = 10*a(n-1) for n > 3.
a(n) = A096363(n)/5. (End)
EXAMPLE
L(i) mod 10 = L(i+12) mod 10; L(i) mod 10^2 = L(i+a(2)) mod 10^2; L(i) mod 10^3 = L(i+a(3)) mod 10^3;
MATHEMATICA
LinearRecurrence[{10}, {12, 60, 300}, 25] (* Paolo Xausa, Mar 30 2026 *)
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jerzy Podgorski (j.podgorski(AT)pollub.pl), May 14 2006; corrected May 16 2006
EXTENSIONS
More terms from Max Alekseyev, May 17 2006
STATUS
approved
