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Search: id:A053664
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| A053664 |
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Smallest number m such that m = i mod prime_i for 1<=i<=n. |
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+0
10
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| 1, 5, 23, 53, 1523, 29243, 299513, 4383593, 188677703, 5765999453, 5765999453, 2211931390883, 165468170356703, 8075975022064163, 361310530977154973, 20037783573808880093, 1779852341342071295513, 40235059344426324076913
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Suggested by Chinese Remainder Theorem.
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REFERENCES
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Niven & Zuckerman: An Intr. to the Theory of Numbers John Wiley 1966. Pag. 40
Paulo Ribenboim : The New Book of Prime Numbers Records Springer 1996 Pag. 33
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LINKS
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Nick Hobson, Table of n, a(n) for n = 1..100
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EXAMPLE
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a(3) = 23 because this is the smallest number m such that m = 1 mod 2, m = 2 mod 3 and m = 3 mod 5.
a(4) = 53 because 53 - 1 is divisible by 2, 53 - 2 is divisible by 3, 53 - 3 is divisible by 5 and 53 - 4 is divisible by 7.
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MATHEMATICA
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f[n_] := Block[{a = Table[ i, {i, n}], b = Table[ Prime[i], {i, n}]}, Return[ ChineseRemainder[a, b]]]; Table[ f[n], {n, 1, 20}]
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PROGRAM
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(PARI) for(n=1, 20, m=1; while(sum(i=1, n, abs(m%prime(i)-i))>0, m++); print1(m, ", "))
(PARI) x=Mod(1, 1); for(i=1, 18, x=chinese(x, Mod(i, prime(i))); print1(component(x, 2), ", ")) - Nick Hobson (nickh(AT)qbyte.org), Jan 08 2007
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CROSSREFS
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Sequence in context: A082277 A155851 A019267 this_sequence A092544 A098499 A075565
Adjacent sequences: A053661 A053662 A053663 this_sequence A053665 A053666 A053667
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Joe K. Crump (joecr(AT)carolina.rr.com), Feb 16 2000
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EXTENSIONS
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Additional comments from Luis A. Rodriguez (luiroto(AT)yahoo.com), Apr 23 2002
Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), May 03 2002
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