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

1,1

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).

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001043, A001358, A005117, A206462.

Sequence in context: A222463 A097252 A169610 * A043886 A044463 A270811

Adjacent sequences: A206326 A206327 A206328 * A206330 A206331 A206332

Keyword

nonn

Author

Zak Seidov, Feb 06 2012

Status

approved