A383636 Integers k such that there is no prime of the form x*y+1 with x+y=k.

1, 6, 30, 54

Offset: 1

Author

Michel Marcus, May 03 2025

Keywords

• nonn
• hard

Comments

If k is odd, one of x or y is even. If k is even, there are cases where both x and y are odd. There is no need to check them, since we know in advance that x*y + 1 is even. - Ivan N. Ianakiev, May 04 2025

It is very likely that there are no further terms.

Crossrefs

Cf. A026728, A109905.

Programs

Mathematica

fQ[n_]:=If[OddQ[n],Select[Range[n/2],PrimeQ[(#*(n-#))+1]&]=={},Select[Range[2,n/2,2],PrimeQ[(#*(n-#))+1]&]=={}]; Select[Range[100],fQ] (* Ivan N. Ianakiev, May 04 2025 *)

PARI

isok(k) = for(i=1, k\2, if(isprime(i*(k-i)+1), return(0))); 1;