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Search: id:A049296
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| A049296 |
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First differences of A008364. Also first differences of reduced residue system (RRS) for 4th primorial number, A002110(4)=210. |
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+0
7
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| 10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 2, 10, 2, 4, 2, 4, 6, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First differences of reduced residue systems modulo primorial numbers are essentially palindromic + 1 separator term (2). The palindromic part starts and ends with p_(n+1)-1 for the n-th primorial number.
This sequence has period A005867(4)=A000010(A002110(4))=48. The 0th, first, 2nd and 3rd similar difference sequences are as follows: {1},{2},{4,2},{6,4,2,4,2,4,6,2} obtained from reduced residue systems of consecutive primorials.
Difference sequence of the "4th diatomic sequence" - A. de Polignac (1849), J. Dechamps (1907).
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REFERENCES
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Dickson L. E., History of the Theory of Numbers, Vol. 1, p. 439, Chelsea, 1952.
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MATHEMATICA
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t1=Table[ GCD[ w, 210 ], {w, 1, 210} ] /t2=Flatten[ Position[ t1, 1 ] ] /t3=Mod[ RotateLeft[ t2 ]-t2, 210 ]
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CROSSREFS
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Cf. A005867, A008364, A002110, A001223.
Sequence in context: A136712 A138999 A010175 this_sequence A069036 A037922 A111287
Adjacent sequences: A049293 A049294 A049295 this_sequence A049297 A049298 A049299
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
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Corrected by Frederic Devaux, Feb 02 2007
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