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Search: id:A116151
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| A116151 |
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a(n) = smallest positive integer x satisfying the system of congruences x == 1 (mod 2), x == 2 (mod 3), x == 3 (mod 5), x == 5 (mod 7), ..., x == p[n-1] (mod p[n]), where p[n] is the n-th prime number and p[0] taken to be 1. |
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+0
2
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| 1, 5, 23, 173, 2273, 2273, 452723, 6578843, 113275433, 3682761353, 10152454583, 5024164707833, 249908523156563, 5726413266646343, 345878207890067123, 15103232990013860963, 1905274424667036455303, 111502614383457156882293
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Minimum Chinese Remainder Prime Modulus Ladder: for the n-th term, the number modulus a prime equals the previous prime for the first n primes (the inital term is defined as 1). - Fred Schneider (frederick.william.schneider(AT)gmail.com), Oct 21 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
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EXAMPLE
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a(3)=23 because that is the smallest number such that n%2 = 1, n%3 = 2 and n%5 = 3
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PROGRAM
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(PARI) { a(n) = lift(chinese(vector(n, i, Mod(if(i==1, 1, prime(i-1)), prime(i))))) }; vector(30, n, a(n)) [Max Alekseyev, Apr 16 2007]
(PARI) z=Mod(1, 2); forprime(x=3, 100, z=chinese(z, Mod(precprime(x-1), x)); print(lift(z)) - Fred Schneider (frederick.william.schneider(AT)gmail.com), Oct 21 2007
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CROSSREFS
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Sequence in context: A007836 A054749 A107204 this_sequence A116652 A072104 A086797
Adjacent sequences: A116148 A116149 A116150 this_sequence A116152 A116153 A116154
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KEYWORD
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nonn
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AUTHOR
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Christian Bjartli (cbjartli(AT)gmail.com), Apr 14 2007
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EXTENSIONS
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More terms from Max Alekseyev, Apr 16 2007
Edited by njas, May 05 2007
Further edited by njas, Jun 30 2008 at the suggestion of R. J. Mathar and Christian Bjartli.
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