login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026728 a(n) = number of primes of the form k*(n-k) + 1. 5
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; text; internal format)
OFFSET

1,5

COMMENTS

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

LINKS

Table of n, a(n) for n=1..95.

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.

MATHEMATICA

a[n_] := Select[(Times @@ # + 1&) /@ IntegerPartitions[n, {2}], PrimeQ] // Length;

Array[a, 95] (* Jean-Fran├žois Alcover, Aug 02 2018 *)

PROG

(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: A292108 A342176 A325195 * A241556 A242029 A090722

Adjacent sequences:  A026725 A026726 A026727 * A026729 A026730 A026731

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 27 2004

EXTENSIONS

More terms from Max Alekseyev, Oct 04 2005

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 10 22:20 EDT 2021. Contains 342856 sequences. (Running on oeis4.)