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A157752
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Smallest positive integer m such that m == prime(i) (mod prime(i+1)) for all 1<=i<=n.
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4
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2, 8, 68, 1118, 2273, 197468, 1728998, 1728998, 447914738, 10152454583, 1313795640428, 97783391392958, 5726413266646343, 38433316595821418, 15103232990013860963, 943894249589930135768, 52858423703753671390658, 932521283899305953765183, 8790842834979573009644273
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OFFSET
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1,1
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COMMENTS
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Suggested by Chinese Remainder Theorem.
a(n) is prime for n = 1, 5, 10, 23, 30.
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LINKS
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MAPLE
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local lrem, leval, i ;
lrem := [] ;
leval := [] ;
for i from 1 to n do
lrem := [op(lrem), ithprime(i+1)] ;
leval := [op(leval), ithprime(i)] ;
end do:
chrem(leval, lrem) ;
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MATHEMATICA
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a[n_] := ChineseRemainder[Prime[Range[n]], Prime[Range[2, n + 1]]] a[ # ] & /@ Range[30]
Table[With[{pr=Prime[Range[n]]}, ChineseRemainder[Most[pr], Rest[pr]]], {n, 2, 30}] (* Harvey P. Dale, Jun 11 2017 *)
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PROG
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(PARI) x=Mod(1, 1); for(i=1, 20, x=chinese(x, Mod(prime(i), prime(i+1))); print1(component(x, 2), ", "))
(Python)
from sympy.ntheory.modular import crt
from sympy import prime
def A157752(n): return int(crt((s:=[prime(i+1) for i in range(1, n)])+[prime(n+1)], [2]+s)[0]) # Chai Wah Wu, May 02 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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