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A285086
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Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime.
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8
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OFFSET
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1,2
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COMMENTS
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Because asymptotically A000041(n^2+1) ~ exp(Pi*sqrt(2/3*(n^2+1))) / (4*sqrt(3)*(n^2+1)), the sum of the prime probabilities ~ 1/log(A000041(n^2+1)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.
a(4) > 90000.
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LINKS
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EXAMPLE
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a(2) = 2 is in the sequence because A000041(2^2+1) = 7 is a prime.
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PROG
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(PARI) for(n=1, 3920, if(ispseudoprime(numbpart(n^2+1)), print1(n, ", ")))
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CROSSREFS
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KEYWORD
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nonn,hard,more,bref
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AUTHOR
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STATUS
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approved
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