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A214149 Least prime p such that the factorization of p^2-9 contains n consecutive primes beginning with prime(3)=5.

%I A214149 #24 Jun 02 2022 16:48:48
%S A214149 7,17,157,283,20023,20023,6446437,14382547,122862737,12925003913,
%T A214149 625586209427,761375971073,92757861866387,15447055149567577,
%U A214149 192604162645538927,192604162645538927,724012906264106939197,2667069644892918607163,235168333030918497994787
%N A214149 Least prime p such that the factorization of p^2-9 contains n consecutive primes beginning with prime(3)=5.
%C A214149 We consider prime-smoothness for primes >=5, because primes p>3 are not divisible by 3, and so p-3 and p+3 are not divisible by 3.
%H A214149 Chai Wah Wu, <a href="/A214149/b214149.txt">Table of n, a(n) for n = 1..29</a>
%e A214149 20020 = 2^2*5*7*11*13, 20026 = 2*17*19*31; 20023^2-9 contains 6 all-consecutive primes beginning with 5.
%e A214149 6446437^2-9 = 2^4*5*7^2*11*13*17^2*19*23*587 contains 7 all-consecutive primes, the first one being 5.
%o A214149 (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++ ; ) }
%o A214149 (Python)
%o A214149 from itertools import product
%o A214149 from sympy import isprime, sieve, prime
%o A214149 from sympy.ntheory.modular import crt
%o A214149 def A214149(n): return 7 if n == 1 else int(min(filter(lambda n: n > 3 and isprime(n),(crt(tuple(sieve.primerange(5,prime(n+2)+1)), t)[0] for t in product((3,-3),repeat=n))))) # _Chai Wah Wu_, Jun 01 2022
%Y A214149 Cf. A214089, A214150.
%K A214149 nonn
%O A214149 1,1
%A A214149 _Robin Garcia_, Jul 05 2012
%E A214149 More terms from _Max Alekseyev_, Aug 22 2012