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A114307
Length of the cycle for Lucas numbers mod 10^n.
1
12, 60, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000, 30000000000000, 300000000000000, 3000000000000000, 30000000000000000, 300000000000000000, 3000000000000000000
OFFSET
1,1
COMMENTS
This is the length of the cycle for final n decimal digits in Lucas numbers (A000032)
LINKS
Eric Weisstein's World of Mathematics, Lucas Number
FORMULA
a(1)=12, a(2)=60, a(n)=3*10^(n-1) for n>2.
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
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;
CROSSREFS
KEYWORD
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