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A208645 Least x>0 such that x^2+x+n is not prime.

%I A208645 #25 May 30 2025 23:14:14
%S A208645 2,4,1,2,1,4,1,1,1,2,1,10,1,1,1,2,1,16,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,
%T A208645 1,1,4,1,1,1,2,1,40,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,3,1,
%U A208645 1,1,2,1,2,1,1,1,1,1,6,1,1,1,2,1,1,1,1
%N A208645 Least x>0 such that x^2+x+n is not prime.
%C A208645 By definition, a(n)>0 for all n, and a(n)>1 if n+2 is prime.
%H A208645 Charles R Greathouse IV, <a href="/A208645/b208645.txt">Table of n, a(n) for n = 0..10000</a>
%e A208645 a(0)=2 since 1^2+1+0=2 is prime, but 2^2+2+0=6 is composite.
%e A208645 a(1)=4 since 1^2+1+1=2, 2^2+2+1=7 and 3^2+3+1=13 are prime, but 4^2+4+1=21 is composite.
%t A208645 lx[n_]:=Module[{x=1},While[PrimeQ[x^2+x+n],x++];x]; Array[lx, 90, 0] (* _Harvey P. Dale_, Aug 14 2013 *)
%o A208645 (PARI) a(n)=for( x=1, n+3, isprime(x^2+x+n) || return(x))
%Y A208645 Cf. A208936, A014556, A092749.
%Y A208645 Cf. A117530, A117531.
%K A208645 nonn
%O A208645 0,1
%A A208645 _M. F. Hasler_, Mar 03 2012