A109908 -id:A109908 - 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

A109907 Beginning with 7, a(n+1) = greatest prime of the form k*{a(n)-k}-1. If no prime is obtained the sequence ends at that point.

Original entry on oeis.org

7, 11, 29, 197, 9689, 23469167, 137700449916401, 4740353476794815041972197893, 5617737771240172767652929826457529708578746492288409399, 7889744416604625924469156192031986939513870147397674409917489724005347434748024264638497225986334149357868007

Offset: 0

Amarnath Murthy, Jul 15 2005

nonn

Conjecture: The sequence is infinite.

Cf. A109904, A109905, A026728, A109908, A109909.

{ b(n) = forstep(k=n\2,1,-1,if(isprime(k*(n-k)-1),return(k*(n-k)-1)));return(0) }
my(s=7); while(1,print1(s,", ");s=b(s)) \\ Max Alekseyev, Oct 04 2005

More terms from Max Alekseyev, Oct 04 2005

cp's OEIS Frontend

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

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