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a(n) = greatest prime of the form k*(n-k)-1, or 0 if no such prime exists.
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%I #14 Jul 24 2023 01:23:34

%S 0,0,0,3,5,7,11,11,19,23,29,31,41,47,53,59,71,79,89,83,109,71,131,139,

%T 149,167,181,191,197,223,239,251,271,263,293,307,311,359,379,383,419,

%U 439,461,479,503,503,521,571,599,599,647,659,701,727,743,719,811,839

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

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

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

%o (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

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

%K nonn,easy

%O 1,4

%A _Amarnath Murthy_, Jul 15 2005

%E More terms from _Max Alekseyev_, Oct 04 2005

%E Definition corrected by _David Wasserman_, Oct 28 2008