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Search: id:A127699
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| A127699 |
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Length of period of the sequence (1^1^1^..., 2^2^2^..., 3^3^3^..., 4^4^4^..., ...) modulo n. |
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+0
1
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| 1, 2, 6, 4, 20, 6, 42, 8, 18, 20, 220, 12, 156, 42, 120, 16, 272, 18, 342, 40, 84, 220, 5060, 24, 200, 156, 54, 84, 2436, 120
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For any positive integers a and m the sequence a, a^a, a^a^a, a^a^a^a,... becomes eventually constant modulo m. So the remainder of a^a^a^... modulo n is well defined.
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FORMULA
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a(n) = lcm(n, a(phi(n))), where phi is Euler's totient function.
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EXAMPLE
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a(10)=20 because the last digit of 1^1^1^.. is 1; the sequence 2,2^2,2^2^2,.. ends with 2,4,6,6,...; the sequence 3,3^3,3^3^3,... with 3,7,7,...; 4,4^4,4^4^4,... with 4,6,6,...; and so on. We get as last digits 1,6,7,6,5,6,3,6,9,0, 1,6,3,6,5,6,7,6,9,0 and then the pattern repeats.
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CROSSREFS
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Cf. A000010.
Sequence in context: A100695 A100140 A009262 this_sequence A124838 A088659 A052100
Adjacent sequences: A127696 A127697 A127698 this_sequence A127700 A127701 A127702
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KEYWORD
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easy,nonn
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AUTHOR
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Jan Fricke (jfricke(AT)math.uni-jena.de), Apr 11 2007
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