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A309289
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Numbers k such that binomial(2k,k) - k^2 is prime.
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2
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2, 3, 5, 9, 13, 27, 47, 59, 111, 547, 923, 1301, 2263, 5189
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OFFSET
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1,1
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COMMENTS
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If a term k > 2 is divisible by a prime p, then all digits in the base-p expansion of k are less than p/2. In particular, 2 is the only even term. - Robert Israel, Aug 02 2019
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LINKS
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MAPLE
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filter:= t -> isprime(binomial(2*t, t)-t^2):
select(filter, [2, seq(i, i=3..6000, 2)]); # Robert Israel, Aug 02 2019
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PROG
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(PARI) is(n)=ispseudoprime(binomial(2*n, n)-n^2)
for(n=0, oo, is(n) && print1(n, ", "))
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CROSSREFS
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Cf. A309290 (binomial(k^2,k) - k^2 is squarefree).
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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