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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A204895 A064652 A077600 * A282691 A346744 A265577

Adjacent sequences: A120220 A120221 A120222 * A120224 A120225 A120226

Keyword

nonn

Author

Zak Seidov, Jun 10 2006

Status

approved