login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A109905
a(n) = greatest prime of the form k*(n-k) +1. 0 if no such prime exists.
6
0, 2, 3, 5, 7, 0, 13, 17, 19, 17, 31, 37, 43, 41, 37, 61, 73, 73, 89, 101, 109, 113, 131, 109, 157, 89, 181, 197, 211, 0, 241, 257, 271, 281, 307, 181, 337, 353, 379, 401, 421, 433, 463, 449, 487, 521, 547, 577, 601, 617, 631, 677, 701, 0, 757, 769, 811, 761, 859, 757
OFFSET
1,2
COMMENTS
k can take values from 1 to floor[n/2].
a(n)=0 for k = 1, 6, 30 and 54. Are there any others? - Robert Israel, Feb 23 2018
There are none for n up to 10^9. - Mauro Fiorentini, Jul 24 2023
LINKS
EXAMPLE
a(15) = 37 as 1*14 +1 = 16, 2*13 +1 = 27 are composite but 3*12 +1= 37 is a prime.
a(6) = 0 as 1*5 +1=6, 2*4 +1=9, 3*3 +1 = 10 are all composite.
MAPLE
f:= proc(n) local k;
for k from floor(n/2) to 1 by -1 do
if isprime(k*(n-k)+1) then return k*(n-k)+1 fi
od:
0 end proc:
map(f, [$1..100]); # Robert Israel, Feb 23 2018
MATHEMATICA
Table[Max@Prepend[Select[Table[k (n - k) + 1, {k, n/2}], PrimeQ], 0], {n, 60}] (* Ivan Neretin, Feb 23 2018 *)
PROG
(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
CROSSREFS
Sequence in context: A171013 A020919 A126053 * A230200 A113493 A060420
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 15 2005
EXTENSIONS
More terms from Max Alekseyev, Oct 04 2005
STATUS
approved