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A152765
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Smallest prime divisor of Catalan number A000108(n), with a(0) = a(1) = 1.
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3
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1, 1, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
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OFFSET
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0,3
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COMMENTS
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a(n) <> 2 iff n = 2^k - 1 (A000225). In fact for k>1, a(2^k-1): 5, 3, 3, 7, 3, 3, 7, 3, 3, 3, 3, 3, 3, ..., . (A120275) - Robert G. Wilson v, Nov 14 2015
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LINKS
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FORMULA
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MATHEMATICA
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FactorInteger[#][[1, 1]]&/@CatalanNumber[Range[2, 80]] (* Harvey P. Dale, Oct 08 2014 *)
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PROG
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(PARI) a(n) = if (n<=1, 1, factor(binomial(2*n, n)/(n+1))[1, 1]); \\ Michel Marcus, Nov 14 2015; corrected Jun 13 2022
(PARI) A152765(n) = if(n<2, 1, my(c=binomial(2*n, n)/(n+1)); forprime(p=2, oo, if(!(c%p), return(p)))); \\ Antti Karttunen, Jan 12 2019
(Magma) [Minimum(PrimeDivisors(Catalan(n))): n in [2..100]]; // Vincenzo Librandi, Jan 04 2017
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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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Terms a(0) = a(1) = 1 prepended and more terms added by Antti Karttunen, Jan 12 2019
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STATUS
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approved
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