A114307 Length of the cycle for Lucas numbers mod 10^n.

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

Table of n, a(n) for n=1..19.

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

Cf. A000032, A096363, A001175.

Sequence in context: A074433 A280175 A216491 * A009031 A009136 A053533

Adjacent sequences: A114304 A114305 A114306 * A114308 A114309 A114310

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