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%I #39 Jan 16 2024 08:11:49
%S 6,30,42,102,138,282,462,570,618,642,822,858,1230,1290,1302,1482,1698,
%T 1722,1878,2082,2130,2238,2310,2382,2658,2730,2802,3390,3462,3558,
%U 3918,3930,4002,4218,4242,4422,4638,4722,5010,5442,5478,5502,5658,6090,6198
%N Squarefree numbers sandwiched between a pair of twin primes.
%C Numbers k such that k is squarefree, k-1 and k+1 are primes.
%C Intersection of A005117 and A014574. - _Michel Marcus_, Mar 06 2014
%C Also, intersection of A077064 and A077067. - _Zak Seidov_, Mar 20 2016
%C All terms are multiples of 6. - _Zak Seidov_, Mar 20 2016
%C All terms == 6 (mod 12). - _Robert Israel_, Mar 21 2016
%H Robert Israel, <a href="/A070195/b070195.txt">Table of n, a(n) for n = 1..10000</a>
%p select(t -> numtheory:-issqrfree(t) and isprime(t+1) and isprime(t-1),
%p [seq(i, i=6..10000, 12)]); # _Robert Israel_, Mar 21 2016
%t Select[12 * Range[0, 500] + 6, PrimeQ[#-1] && PrimeQ[#+1] && SquareFreeQ[#] &] (* _Amiram Eldar_, May 23 2022 *)
%o (PARI) {forstep(n=6,8000,12,if(issquarefree(n)&&isprime(n-1)&&isprime(n+1),print1(n",")));} \\ _Zak Seidov_, Mar 20 2016
%Y Cf. A005117, A014574, A077064, A077067. - _Zak Seidov_, Mar 20 2016
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_ and _Labos Elemer_, May 06 2002
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