A206329 Squarefree sums of 2 successive primes.

5, 30, 42, 78, 138, 186, 210, 222, 258, 330, 390, 410, 434, 462, 618, 762, 786, 798, 906, 930, 946, 966, 978, 1002, 1030, 1230, 1290, 1334, 1374, 1410, 1446, 1482, 1518, 1542, 1606, 1722, 1758, 1770, 1794, 1830, 1866, 1878, 1938, 1974, 2006, 2022, 2190, 2226

Offset: 1

Author

Zak Seidov, Feb 06 2012

Keywords

• nonn

Comments

Intersection of A001043 and A005117, both infinite, but is their intersection infinite?

Also note that the only prime is a(1)=5 and there are no semiprimes (products of 2 primes A001358).

Examples

			a(1)=5=A001043(1)=A005117(4), a(2)=30=A001043(6)=A005117(19), a(3)=42=A001043(8)=A005117(28).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001043, A001358, A005117, A206462.

Programs

Maple

N:= 1000: # to get the first N terms
count:= 0:
p:= 2:
while count < N do
  pp:= nextprime(p);
  if numtheory:-issqrfree(p+pp) then
    count:= count+1;
    A[count]:= p+pp;
  fi;
  p:= pp;
od:
seq(A[i],i=1..N);
# Robert Israel, Jul 20 2014

Mathematica

Select[Table[Prime[n] + Prime[n + 1], {n, 300}], SquareFreeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2012 *)

PARI

p=2;forprime(q=3,1e4,if(issquarefree(p+q),print1(p+q", "));p=q) \\ Charles R Greathouse IV, Feb 08 2012