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A206329 Squarefree sums of 2 successive primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Moshe Levin, Feb 06 2012

STATUS

approved

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Last modified August 23 19:19 EDT 2017. Contains 291021 sequences.