A085063 a(n) is the minimal number k such that n+k and n*k+1 are primes.

1, 1, 2, 1, 2, 1, 4, 5, 2, 1, 2, 1, 4, 3, 2, 1, 6, 1, 10, 3, 2, 1, 6, 13, 4, 3, 4, 1, 2, 1, 10, 11, 10, 3, 2, 1, 4, 5, 2, 1, 2, 1, 4, 9, 14, 1, 6, 5, 4, 3, 2, 1, 14, 5, 6, 5, 4, 1, 12, 1, 6, 5, 10, 3, 2, 1, 4, 15, 2, 1, 8, 1, 6, 27, 8, 3, 6, 1, 4, 3, 2, 1, 6, 5, 12, 11, 20, 1, 12, 7, 6, 5, 4, 3, 2, 1, 4, 5

Offset: 1

Author

Amarnath Murthy, Jun 28 2003

Keywords

• nonn

Comments

If n+1 is prime then a(n)=1; if n+1 is not prime then a(n)=A120223(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. A092945, A120223, A120224, A120225.

Programs

Maple

f:= proc(n) local k;
for k from 1+(n mod 2) by 2 do
  if isprime(n+k) and isprime(n*k+1) then return k fi
od
end proc:
f(1):= 1: # Robert Israel, May 14 2018

Mathematica

Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True,True},Sow[x];Break[]],{x,1,100}],{n,120}]][[2,1]]
nkp[n_]:=Module[{k=1},While[!And@@PrimeQ[{n+k,n*k+1}],k++];k]; Array[nkp, 100] (* Harvey P. Dale, Apr 11 2012 *)

PARI

a(n) = {my(k=1); while (!isprime(n+k) || !isprime(n*k+1), k++); k;} \\ Michel Marcus, May 14 2018

Extensions

Corrected and extended by Zak Seidov, Jun 10 2006