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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. 2

%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^2-9 contains n consecutive primes beginning with prime(3)=5.

%C 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.

%e 20020 = 2^2*5*7*11*13, 20026 = 2*17*19*31; 20023^2-9 contains 6 all-consecutive primes beginning with 5.

%e 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 (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

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Last modified December 4 15:27 EST 2020. Contains 338927 sequences. (Running on oeis4.)