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%I #29 Oct 30 2018 10:31:02
%S 5,30,42,78,138,186,210,222,258,330,390,410,434,462,618,762,786,798,
%T 906,930,946,966,978,1002,1030,1230,1290,1334,1374,1410,1446,1482,
%U 1518,1542,1606,1722,1758,1770,1794,1830,1866,1878,1938,1974,2006,2022,2190,2226
%N Squarefree sums of 2 successive primes.
%C Intersection of A001043 and A005117, both infinite, but is their intersection infinite?
%C Also note that the only prime is a(1)=5 and there are no semiprimes (products of 2 primes A001358).
%H Charles R Greathouse IV, <a href="/A206329/b206329.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=5=A001043(1)=A005117(4), a(2)=30=A001043(6)=A005117(19), a(3)=42=A001043(8)=A005117(28).
%p N:= 1000: # to get the first N terms
%p count:= 0:
%p p:= 2:
%p while count < N do
%p pp:= nextprime(p);
%p if numtheory:-issqrfree(p+pp) then
%p count:= count+1;
%p A[count]:= p+pp;
%p fi;
%p p:= pp;
%p od:
%p seq(A[i],i=1..N);
%p # _Robert Israel_, Jul 20 2014
%t Select[Table[Prime[n] + Prime[n + 1], {n, 300}], SquareFreeQ] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2012 *)
%o (PARI) p=2;forprime(q=3,1e4,if(issquarefree(p+q),print1(p+q", "));p=q) \\ _Charles R Greathouse IV_, Feb 08 2012
%Y Cf. A001043, A001358, A005117, A206462.
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 06 2012
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