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A355956
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Index k of partition function p such that p(k) is a member of a cousin prime pair.
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0
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3, 5, 6, 13, 36, 157, 302, 546, 2502, 2732, 19439060
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OFFSET
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1,1
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COMMENTS
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Because asymptotically the size of the partition number function p(n) ~ O(exp(sqrt(n))), and the probability of primality of p(n) ~ O(1/sqrt(n)) and the combined probability of primality of p(n) and p(n)+-4 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(12) > 4*10^7.
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LINKS
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EXAMPLE
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5 is in the sequence because A000041(5) = 7 and 7 + 4 = 11 are cousin primes.
13 is in the sequence because A000041(13) = 101 and 101 - 4 = 97 are cousin primes.
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PROG
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(PARI) for(n=1, 10000, if(ispseudoprime(p=numbpart(n))&&(ispseudoprime(p-4)||ispseudoprime(p+4)), 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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