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A059865
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Product(p(i)-6), i=4,5...n.
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5
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1, 1, 1, 1, 5, 35, 385, 5005, 85085, 1956955, 48923875, 1516640125, 53082404375, 1964048961875, 80526007436875, 3784722349533125, 200590284525255625, 11032465648889059375, 672980404582232621875, 43743726297845120421875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Arises in Hardy-Littlewood prime k-tuplet conjectural formulas. Also the sequence gives the exact numbers of X42424Y difference-pattern in dRRS[m], where m=modulus=A002110(n). See A049296 (=dRRS[210]=list of first differences of reduced residue system modulo 210=4th primorial). A pattern X42424Y corresponds to a residue-sextuple or it is their difference-quintuple, X,Y>4. Analogous pattern for primes is in A022008.
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REFERENCES
| See A059862 for references.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.
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LINKS
| C. K. Caldwell, Prime k-tuple Conjecture
S. R. Finch, Hardy-Littlewood Constants
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
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EXAMPLE
| {p-6}={-4,-3,-1,1,5,7,11..}={1,1,1,1,5,7,11,..}; a(7)=Apply[Times,{1,1,1,1,5,7,11}]=385. Also in one period of dRRS with 2,6,30,210,2310,.. modulus [A002110(n)] 1,2,8,48,480,..differences occur [A005867(n)]. The number of X42424Y residue-difference-patterns are 0,1,1,1,5,.. respectively starting at suitable residues coprime to A002110(n).
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CROSSREFS
| Cf. A049296, A002110, A005867, A000847, A022008, A051160-A051168, A048298, A059861-A059865.
Sequence in context: A201367 A125864 A204290 * A097492 A125802 A034217
Adjacent sequences: A059862 A059863 A059864 * A059866 A059867 A059868
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 28 2001
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