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
Chai Wah Wu, Table of n, a(n) for n = 1..29
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++ ; ) }
(Python)
from itertools import product
from sympy import isprime, sieve, prime
from sympy.ntheory.modular import crt
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Garcia, Jul 05 2012
EXTENSIONS
More terms from Max Alekseyev, Aug 22 2012
STATUS
approved