A120224 a(n) is the minimal number k>=n such that n+k and n*k+1 are primes.

1, 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 A120225 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, A120225.

Programs

Mathematica

Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True,True},Sow[x];Break[]],{x, n,1000}],{n,120}]][[2,1]]
mnk[n_]:=Module[{k=n},Until[AllTrue[{n+k,n*k+1},PrimeQ],k++];k]; Join[{1},Array[mnk,80,2]] (* Harvey P. Dale, May 12 2025 *)