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Search: id:A066853
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| A066853 |
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Number of different remainders (or residues) for the Fibonacci numbers (A000045) when divided by n (i.e. the size of the set of F(i) mod n over all i). |
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5
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| 1, 2, 3, 4, 5, 6, 7, 6, 9, 10, 7, 11, 9, 14, 15, 11, 13, 11, 12, 20, 9, 14, 19, 13, 25, 18, 27, 21, 10, 30, 19, 21, 19, 13, 35, 15, 29, 13, 25, 30, 19, 18, 33, 20, 45, 21, 15, 15, 37, 50, 35, 30, 37, 29, 12, 25, 33, 20, 37, 55, 25, 21, 23, 42, 45, 38, 51, 20, 29, 70, 44, 15, 57
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The Fibonacci numbers mod n for any n are periodic - see A001175 for period lengths. - Ron Knott (ron(AT)ronknott.com), Jan 05 2005
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EXAMPLE
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a(8)=6 since the Fibonacci numbers, 0,1,1,2,3,5,8,13,21,34,55,89,144,.. when divided by 8 have remainders 0,1,1,2,3,5,0,5,5,2,7,1 (repeatedly) which only contains the remainders 0,1,2,3,5 and 7, i.e. 6 remainders, so a(8)=6
a(11)=7 since Fibonacci numbers reduced modulo 11 are {0, 1, 2, 3, 5, 8, 10}.
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CROSSREFS
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Cf. A001175, A079002.
Sequence in context: A005599 A071934 A161658 this_sequence A141258 A117656 A101918
Adjacent sequences: A066850 A066851 A066852 this_sequence A066854 A066855 A066856
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KEYWORD
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nonn
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AUTHOR
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Reiner Martin (reinermartin(AT)hotmail.com), Jan 21 2002
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