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A084360
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Number of partitions of n into pair of parts whose difference is a prime.
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1
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0, 0, 0, 1, 1, 1, 2, 1, 3, 1, 3, 1, 4, 1, 5, 1, 5, 1, 6, 1, 7, 1, 7, 1, 8, 1, 8, 1, 8, 1, 9, 1, 10, 1, 10, 1, 10, 1, 11, 1, 11, 1, 12, 1, 13, 1, 13, 1, 14, 1, 14, 1, 14, 1, 15, 1, 15, 1, 15, 1, 16, 1, 17, 1, 17, 1, 17, 1, 18, 1, 18, 1, 19, 1, 20, 1, 20, 1, 20, 1, 21, 1, 21, 1, 22, 1, 22, 1, 22, 1
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OFFSET
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1,7
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COMMENTS
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Order of set A = { (p,q): p+q = n, q>=p and q-p is a prime}.
a(1) = a(2) = 0; for even n >= 4, a(n) = 1; for odd n >= 3, a(n) = pi(n-1) - 1, where pi(n) = A000720(n) is the prime counting function. - Wesley Ivan Hurt, Feb 01 2013
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LINKS
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FORMULA
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a(n) = ( pi(n-1)-2 )*( n mod 2 ) + 1 + floor(1/n) - floor(n/2)*floor(2/n). - Wesley Ivan Hurt, Feb 01 2013
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EXAMPLE
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a(7) = 2 and the partitions are (1,6) and (2,5).
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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