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Search: id:A114307
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| A114307 |
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Length of the cycle for Lucas numbers mod 10^n. |
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+0
1
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| 12, 60, 300, 3000, 30000, 300000, 3000000, 30000000, 300000000, 3000000000, 30000000000, 300000000000, 3000000000000, 30000000000000, 300000000000000, 3000000000000000, 30000000000000000, 300000000000000000, 3000000000000000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is the length of the cycle for final n decimal digits in Lucas numbers (A000032)
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LINKS
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Eric Weisstein's World of Mathematics, Lucas Number
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FORMULA
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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 (maxal(AT)cs.ucsd.edu), May 17 2006
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EXAMPLE
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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;
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CROSSREFS
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Cf. A000032, A096363, A001175.
Sequence in context: A120571 A086950 A074433 this_sequence A009031 A009136 A053533
Adjacent sequences: A114304 A114305 A114306 this_sequence A114308 A114309 A114310
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KEYWORD
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easy,nonn
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AUTHOR
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Jerzy Podgorski (j.podgorski(AT)pollub.pl), May 14 2006; corrected May 16 2006
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EXTENSIONS
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More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), May 17 2006
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