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

1,3

Comments

If n+1 is prime then a(n)=1; if n+1 is not prime then a(n)=A120223(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 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 *)

Prog

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

Crossrefs

Cf. A092945, A120223, A120224, A120225.

Sequence in context: A079499 A166235 A143591 * A263078 A329869 A331188

Adjacent sequences: A085060 A085061 A085062 * A085064 A085065 A085066

Keyword

nonn

Author

Amarnath Murthy, Jun 28 2003

Extensions

Corrected and extended by Zak Seidov, Jun 10 2006

Status

approved