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A268350 Primes p where q = p + 4 is also prime and rad((p+1)(p+2)(p+3)) < pq, where rad(k) is the largest squarefree number dividing k. 1
7, 13, 79, 97, 223, 349, 673, 1087, 1213, 1663, 3697, 13309, 13687, 16927, 20479, 21139, 25999, 32797, 33613, 78649, 122449, 151549, 263167, 401407, 651247, 1058749, 1656247, 1893373, 2060449, 2146687, 3058873, 3276799, 3733207, 3866623, 3880897, 4070197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Are there any consecutive primes p and q for which rad((p+1)(p+2)...(q-1)) < pq with q - p > 4?

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..299

EXAMPLE

79 and 83 are prime, and rad(80*81*82) = rad(2^5*3^4*5*41) = 2*3*5*41 = 1230 < 6557 = 79*83, so 79 is a member of this sequence.

MAPLE

rad:= n -> convert(numtheory:-factorset(n), `*`):

select(p -> isprime(p) and isprime(p+4) and rad((p+1)*(p+2)*(p+3)) < p*(p+4), [seq(i, i=7..10^7, 6)]); # Robert Israel, Feb 05 2016

PROG

(PARI) rad(n)=factorback(factor(n)[, 1])

has(p, q)=if(q-p!=4, return(0)); my(t=rad((p+1)/2)*rad((p+3)/2), pq=p*q); 3*t<pq && rad(p+2)*t<pq

p=2; forprime(q=3, 1e10, if(has(p, q), print1(p", ")); p=q)

CROSSREFS

Subsequence of A029710.

Cf. A078637, A007947.

Sequence in context: A174878 A177198 A177163 * A061521 A073220 A110455

Adjacent sequences:  A268347 A268348 A268349 * A268351 A268352 A268353

KEYWORD

nonn

AUTHOR

J. M. Bergot and Charles R Greathouse IV, Feb 02 2016

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)