A165936 A sequence of triples of squarefree consecutive integers each composed of exactly three primes.

1309, 1310, 1311, 1885, 1886, 1887, 2013, 2014, 2015, 2665, 2666, 2667, 3729, 3730, 3731, 5133, 5134, 5135, 6061, 6062, 6063, 6213, 6214, 6215, 6305, 6306, 6307, 6477, 6478, 6479, 6853, 6854, 6855, 6985, 6986, 6987, 7257, 7258, 7259, 7953, 7954, 7955, 8393

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Formula

a(3n+1) = A066509(n+1); a(3n+2) = 1 + a(3n+1); a(3n+3) = 1 + a(3n+2). - R. J. Mathar, Nov 27 2011

Example

1309 = 7 * 11 * 17, 1310 = 2 * 5 * 131, 1311 = 3 * 19 * 23.

Mathematica

Select[Partition[Range[10000], 3, 1], AllTrue[#, SquareFreeQ]&&Union[ PrimeOmega[ #]] == {3}&]//Flatten (* Harvey P. Dale, Oct 02 2017 *)

Prog

(Magma) a:=[]; f:=func<n|forall{n+s: s in [0, 1, 2] |IsSquarefree(n+s) and #PrimeDivisors(n+s) eq 3}>; for k in [2..8500] do  if f(k) then a:=a cat [k, k+1, k+2]; end if;  end for; a; // Marius A. Burtea, Oct 05 2019

Crossrefs

Sequence in context: A281211 A233975 A209853 * A242606 A066509 A248202

Adjacent sequences: A165933 A165934 A165935 * A165937 A165938 A165939

Keyword

nonn

Author

Richard L. Peterson (rl_pete(AT)yahoo.com), Oct 01 2009

Extensions

More terms from Harvey P. Dale, Oct 02 2017

Status

approved