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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 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 Cf. A214089, A214150. Sequence in context: A364703 A325584 A375426 * A147643 A367809 A061159 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 September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)