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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
7, 17, 157, 283, 20023, 20023, 6446437, 14382547, 122862737, 12925003913, 625586209427, 761375971073, 92757861866387, 15447055149567577, 192604162645538927, 192604162645538927, 724012906264106939197, 2667069644892918607163, 235168333030918497994787 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

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

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.

PROG

(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++ ; ) }

CROSSREFS

Cf. A214089, A214150.

Sequence in context: A227506 A244279 A325584 * A147643 A061159 A178694

Adjacent sequences:  A214146 A214147 A214148 * A214150 A214151 A214152

KEYWORD

nonn

AUTHOR

Robin Garcia, Jul 05 2012

EXTENSIONS

More terms from Max Alekseyev, Aug 22 2012

STATUS

approved

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Last modified October 30 18:13 EDT 2020. Contains 338090 sequences. (Running on oeis4.)