A109907 -id:A109907 - cp's OEIS frontend

A109909 a(n) = number of primes of the form k*(n-k)-1.

0, 0, 0, 2, 2, 1, 2, 1, 4, 1, 3, 2, 3, 2, 3, 2, 4, 3, 5, 1, 10, 1, 5, 5, 4, 2, 6, 3, 5, 3, 9, 4, 11, 3, 5, 5, 5, 5, 14, 1, 6, 6, 7, 6, 11, 5, 8, 4, 15, 3, 13, 4, 10, 9, 6, 5, 11, 4, 12, 5, 13, 4, 12, 4, 6, 11, 13, 4, 12, 6, 15, 12, 9, 4, 9, 5, 10, 8, 10, 3, 28, 7, 11, 15, 6, 9, 20, 7, 20, 6, 17, 5, 23

Offset: 1

Amarnath Murthy, Jul 15 2005

nonn

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

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

Pengcheng Niu and Junli Zhang, On Two Conjectures of A. Murthy, ResearchGate (2024).

Cf. A109904, A109905, A026728, A109907, A109908.

More terms from David Wasserman, Aug 15 2005

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

Original entry on oeis.org

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

Amarnath Murthy, Jul 15 2005

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

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

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

{ 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

More terms from Max Alekseyev, Oct 04 2005

Definition corrected by David Wasserman, Oct 28 2008

cp's OEIS Frontend

A109909 a(n) = number of primes of the form k*(n-k)-1.

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