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A026728
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a(n) = number of primes of the form k*(n-k) + 1.
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5
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0, 1, 1, 1, 2, 0, 3, 2, 1, 1, 4, 1, 6, 1, 1, 2, 8, 1, 5, 3, 1, 4, 7, 1, 7, 1, 4, 5, 8, 0, 10, 6, 2, 2, 7, 1, 9, 8, 4, 4, 14, 1, 16, 3, 3, 5, 12, 3, 7, 7, 4, 11, 21, 0, 11, 4, 7, 6, 11, 2, 12, 9, 7, 10, 7, 1, 22, 7, 7, 5, 17, 3, 23, 10, 2, 9, 19, 2, 19, 8, 5, 8, 23, 1, 16, 6, 4, 11, 14, 4, 16, 12, 9, 5, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Number of primes of form x*y+1 with x+y=n.
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EXAMPLE
| a(7) = 3, 1*6 +1 = 7, 2*5 +1 = 11, 3*4 +1 = 13.
n=16: {m: m=x*y+1 and x+y=16} = {16,29,40,49,56,61,64,65} containing two primes: 29 and 61, therefore a(16)=2.
n = 7 is the only number which gives primes for all possible values of k.
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PROG
| (PARI) { a(n)=local(r); r=0; for(k=1, n\2, if(isprime(k*(n-k)+1), r++)); r } (Alekseyev)
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CROSSREFS
| Cf. A109904, A109905.
Sequence in context: A154752 A194354 A156776 * A090722 A171934 A082785
Adjacent sequences: A026725 A026726 A026727 * A026729 A026730 A026731
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 27 2004
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Oct 04 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2008 at the suggestion of R. J. Mathar
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