A109908 a(n) = greatest prime of the form k*(n-k)-1, or 0 if no such prime exists.

0, 0, 0, 3, 5, 7, 11, 11, 19, 23, 29, 31, 41, 47, 53, 59, 71, 79, 89, 83, 109, 71, 131, 139, 149, 167, 181, 191, 197, 223, 239, 251, 271, 263, 293, 307, 311, 359, 379, 383, 419, 439, 461, 479, 503, 503, 521, 571, 599, 599, 647, 659, 701, 727, 743, 719, 811, 839

Offset: 1

Author

Amarnath Murthy, Jul 15 2005

Keywords

• nonn
• easy

Comments

Conjecture: a(n) > 0 for n > 3.

Conjecture verified up to 10^9. - Mauro Fiorentini, Jul 23 2023

Crossrefs

Cf. A109904, A109905, A026728, A109907, A109909.

Programs

PARI

{ a(n)=forstep(k=n\2,1,-1,if(isprime(k*(n-k)-1),return(k*(n-k)-1)));return(0) } \\ Max Alekseyev, Oct 04 2005

Extensions

More terms from Max Alekseyev, Oct 04 2005

Definition corrected by David Wasserman, Oct 28 2008