A120225 a(n) is the minimal number k>n such that n+k and n*k+1 are primes.

2, 3, 4, 7, 6, 7, 10, 9, 14, 13, 18, 19, 24, 15, 16, 21, 24, 29, 22, 21, 22, 31, 30, 43, 28, 33, 34, 39, 32, 41, 36, 39, 34, 37, 66, 43, 60, 41, 50, 43, 42, 55, 46, 53, 52, 51, 50, 59, 52, 51, 56, 55, 56, 55, 58, 75, 74, 69, 68, 67, 66, 75, 74, 67, 86, 83, 70, 89, 70, 79, 102, 79

Offset: 1

Author

Zak Seidov, Jun 10 2006

Keywords

• nonn

Comments

Differs from A120224 in the first term.

Examples

			a(3)=4 because 3+4=7 and 3*4+1=13 are prime;
a(8)=9 because 8+9=17 and 8*9+1=73 are prime,
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A085063, A092945, A085063, A120223, A120224.

Programs

Mathematica

Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True,True},Sow[x];Break[]],{x, n+1,1000}],{n,120}]][[2,1]]
mnk[n_]:=Module[{k=n+1},While[!AllTrue[{n+k,n*k+1},PrimeQ],k++];k]; Array[ mnk,80] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 15 2015 *)