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%I #14 May 15 2018 06:42:15
%S 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,
%T 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,
%U 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
%N a(n) is the minimal number k such that n+k and n*k+1 are primes.
%C If n+1 is prime then a(n)=1; if n+1 is not prime then a(n)=A120223(n).
%H Robert Israel, <a href="/A085063/b085063.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3)=2 because 3+2=5 and 3*2+1=7 are prime;
%e a(8)=5 because 8+5=13 and 8*5+1=41 are prime,
%p f:= proc(n) local k;
%p for k from 1+(n mod 2) by 2 do
%p if isprime(n+k) and isprime(n*k+1) then return k fi
%p od
%p end proc:
%p f(1):= 1: # _Robert Israel_, May 14 2018
%t Reap[Do[Do[If[PrimeQ[{n+x, n*x+1}]=={True,True},Sow[x];Break[]],{x,1,100}],{n,120}]][[2,1]]
%t nkp[n_]:=Module[{k=1},While[!And@@PrimeQ[{n+k,n*k+1}],k++];k]; Array[nkp, 100] (* _Harvey P. Dale_, Apr 11 2012 *)
%o (PARI) a(n) = {my(k=1); while (!isprime(n+k) || !isprime(n*k+1), k++); k;} \\ _Michel Marcus_, May 14 2018
%Y Cf. A092945, A120223, A120224, A120225.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Jun 28 2003
%E Corrected and extended by _Zak Seidov_, Jun 10 2006
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