A109905 a(n) = greatest prime of the form k*(n-k) +1. 0 if no such prime exists.

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

Ivan Neretin, Table of n, a(n) for n = 1..10000

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

Cf. A109904, A026728.

Sequence in context: A171013 A020919 A126053 * A230200 A113493 A060420

Adjacent sequences: A109902 A109903 A109904 * A109906 A109907 A109908

Keyword

nonn

Author

Amarnath Murthy, Jul 15 2005

Extensions

More terms from Max Alekseyev, Oct 04 2005

Status

approved