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A266366
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Least k such that prime(n) is the smallest odd prime factor of C(2k,k).
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2
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OFFSET
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2,1
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COMMENTS
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If n>0, then a(n+2) >= A129489(n) = least k>1 such that binomial(2k,k) is not divisible by any of the first n odd primes.
It is not known whether any more terms exist. See A129489 for bounds, comments and references.
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LINKS
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EXAMPLE
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C(2,1) = 2, C(4,2) = 6 = 2 * 3, C(6,3) = 20 = 2^2 * 5, and 3 = prime(2), 5 = prime(3), so a(2) = 2 and a(3) = 3.
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PROG
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(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
a(n)=my(q=prime(n), k=1); while(k++, forprime(p=3, q-1, if(valp(2*k, p)>2*valp(k, p), next(2))); if(valp(2*k, q)>2*valp(k, q), return(k))) \\ Charles R Greathouse IV, Feb 03 2016
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CROSSREFS
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KEYWORD
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bref,hard,more,nonn
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AUTHOR
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STATUS
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approved
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