%I #19 May 16 2015 17:40:57
%S 2,3,43,7,163,397,5527,454543,615883,142516687,68967673,57502725253,
%T 37520993053,2630665498987,39809897510563
%N Smallest prime number p such that p + psq(1), p + psq(2), ... p + psq(n) are all prime but p+psq(n+1) is not. (psq(n) is the square of the primorial.)
%e For prime 43, 43 + 4 and 43 + 36 are prime but not 43 + 30^2.
%o (PARI) psq(n)=my(P=1); forprime(p=2, prime(n), P*=p); P^2;
%o isokpsq(p, n) = {for (k=1, n, if (!isprime(p+psq(k)), return (0));); if (!isprime(p+psq(n+1)), return (1));}
%o a(n) = {p = 2; while (!isokpsq(p,n), p = nextprime(p+1)); p;} \\ _Michel Marcus_, May 04 2015
%o (PARI) allprime(v,n=0)=for(i=1,#v,if(!isprime(v[i]+n), return(0))); 1
%o a(n)=if(n<2,return(n+2)); my(t=4,v=vector(n-1,i,t*=prime(i+1)^2),p=2); t*=prime(n+1)^2; forprime(q=3,, if(q-p==4 && allprime(v,p) && !isprime(t+p), return(p)); p=q) \\ _Charles R Greathouse IV_, May 05 2015
%Y Cf. A115786, A034386, A257466.
%K hard,nonn
%O 0,1
%A _Fred Schneider_, Apr 25 2015
%E a(13)-a(14) from _Fred Schneider_, May 16 2015
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