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a(n) = number of primes of the form k*(n-k)-1.
8

%I #13 Sep 29 2024 11:56:45

%S 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,

%T 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,

%U 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

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

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

%C Conjecture verified up to 10^9. - _Mauro Fiorentini_, Jul 23 2023

%H Pengcheng Niu and Junli Zhang, <a href="https://doi.org/10.13140/RG.2.2.16430.11848">On Two Conjectures of A. Murthy</a>, ResearchGate (2024).

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

%K nonn

%O 1,4

%A _Amarnath Murthy_, Jul 15 2005

%E More terms from _David Wasserman_, Aug 15 2005