%I
%S 7,17,157,283,20023,20023,6446437,14382547,122862737,12925003913,
%T 625586209427,761375971073,92757861866387,15447055149567577,
%U 192604162645538927,192604162645538927,724012906264106939197,2667069644892918607163,235168333030918497994787
%N Least prime p such that the factorization of p^29 contains n consecutive primes beginning with prime(3)=5.
%C We consider primesmoothness for primes >=5, because primes p>3 are not divisible by 3, and so p3 and p+3 are not divisible by 3.
%e 20020 = 2^2*5*7*11*13, 20026 = 2*17*19*31; 20023^29 contains 6 allconsecutive primes beginning with 5.
%e 6446437^29 = 2^4*5*7^2*11*13*17^2*19*23*587 contains 7 allconsecutive primes, the first one being 5.
%o (PARI) A214149(n)={ local(a, k=1, p) ; a=prod(j=3, n+2, prime(j)) ; while(1, if( issquare(k*a+9), p=sqrtint(k*a+9) ; if(isprime(p),return(p); ) ; ) ; k++ ; ) }
%Y Cf. A214089, A214150.
%K nonn
%O 1,1
%A _Robin Garcia_, Jul 05 2012
%E More terms from _Max Alekseyev_, Aug 22 2012
