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A355705
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Indices k of partition function p where p(k) and p(k) - 2 are twin primes.
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3
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OFFSET
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1,1
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COMMENTS
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Because asymptotically size of partitions number function p(n) ~ O(exp(sqrt(n))), and probability of primality of p(n) ~ O(1/sqrt(n)) and combined probability of primality of p(n) and p(n)+-2 is ~ O(1/n), the sum of the prime probabilities is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.
a(5) > 10^7.
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LINKS
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EXAMPLE
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4 is a term because A000041(4) = 5, and 3 and 5 are twin primes.
5 is a term because A000041(5) = 7, and 5 and 7 are twin primes.
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PROG
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(PARI) for(n=1, 3600, if(ispseudoprime(p=numbpart(n))&&ispseudoprime(p-2), print1(n, ", ")))
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CROSSREFS
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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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