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A026728 a(n) = number of primes of the form k*(n-k) + 1. +0
6
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; listen)
OFFSET

1,5

COMMENT

Number of primes of form x*y+1 with x+y=n.

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.

PROGRAM

(PARI) { a(n)=local(r); r=0; for(k=1, n\2, if(isprime(k*(n-k)+1), r++)); r } (Alekseyev)

CROSSREFS

Cf. A109904, A109905.

Sequence in context: A097418 A154752 A156776 this_sequence A090722 A082785 A100949

Adjacent sequences: A026725 A026726 A026727 this_sequence A026729 A026730 A026731

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 27 2004

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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Last modified December 16 17:18 EST 2009. Contains 170825 sequences.


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