A120223 a(n) is the minimal number k>1 such that n+k and n*k+1 are primes.

2, 3, 2, 3, 2, 5, 4, 5, 2, 3, 2, 5, 4, 3, 2, 7, 6, 11, 10, 3, 2, 9, 6, 13, 4, 3, 4, 15, 2, 7, 10, 11, 10, 3, 2, 5, 4, 5, 2, 7, 2, 5, 4, 9, 14, 13, 6, 5, 4, 3, 2, 21, 14, 5, 6, 5, 4, 9, 12, 7, 6, 5, 10, 3, 2, 5, 4, 15, 2, 3, 8, 25, 6, 27, 8, 3, 6, 11, 4, 3, 2, 15, 6, 5, 12, 11, 20, 15, 12, 7, 6, 5, 4, 3

Offset: 1

Author

Zak Seidov, Jun 10 2006

Keywords

• nonn

Comments

If n+1 is prime then a(n)>A085063(n); if n+1 is not prime then a(n)=A085063(n).

Examples

			a(3)=2 because 3+2=5 and 3*2+1=7 are prime;
a(8)=5 because 8+5=13 and 8*5+1=41 are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085063, A092945, A085063, A120224, A120225.

Programs

Maple

f:= proc(n) local k;
  for k from `if`( n::odd,2,3) do
     if isprime(n*k+1) and isprime(n+k) then return k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 03 2019

Mathematica

Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True,True},Sow[x];Break[]],{x,2,100}],{n,120}]][[2,1]]
mnk[n_]:=Module[{k=2},While[!AllTrue[{n+k,n*k+1},PrimeQ],k++];k]; Array[ mnk,100] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 15 2014 *)

PARI

for(n=1,100,k=2;while(!isprime(n+k),k++;while(!isprime(n*k+1),k++));print1(k,", ")) \\ Jinyuan Wang, Feb 04 2019