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Search: id:A116515
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| A116515 |
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a(n) = the period of the Fibonacci numbers modulo p divided by the smallest m such that p divides Fibonacci(m), where p is the n-th prime. |
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+0
1
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| 1, 2, 4, 2, 1, 4, 4, 1, 2, 1, 1, 4, 2, 2, 2, 4, 1, 4, 2, 1, 4, 1, 2, 4, 4, 1, 2, 2, 4, 4, 2, 1, 4, 1, 4, 1, 4, 2, 2, 4, 1, 1, 1, 4, 4, 1, 1, 2, 2, 1, 4, 1, 2, 1, 4, 2, 4, 1, 4, 2, 2, 4, 2, 1, 4, 4, 1, 4, 2, 1, 4, 1, 2, 4, 1, 2, 4, 4, 2, 2, 1, 4, 1, 4, 1, 2, 2, 4, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 2, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conditions on p_n mod 4 and mod 5 restrict possible values of a(n). The unknown (?) case is p = 1 mod 4 and (5|p) = 1, equivalently, p = 1 or 9 mod 20, where {1, 2, 4} all occur.
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FORMULA
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a(n) = A060305(n) / A001602(n). a(n) is always one of {1, 2, 4}.
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EXAMPLE
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a(4) = 2, as 7 is the 4th prime, the Fibonacci numbers mod 7 have period 16, the first Fibonacci number divisible by 7 is F(8) = 21 = 3*7, and 16 / 8 = 2.
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CROSSREFS
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Cf. A060305, A001602.
Sequence in context: A079045 A021417 A105791 this_sequence A037178 A113973 A123330
Adjacent sequences: A116512 A116513 A116514 this_sequence A116516 A116517 A116518
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KEYWORD
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easy,nonn
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AUTHOR
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Nick Krempel (ndkrempel(AT)blueyonder.co.uk), Mar 24 2006
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