A263510 Numbers n for which the numbers 6n+1, 3n+2, 6n+7 are all odd composite squarefree numbers, but none are semiprimes.

2121, 3011, 3963, 6125, 7631, 8173, 8275, 8649, 8781, 10519, 10851, 11383, 11599, 11883, 12001, 12163, 12271, 12789, 12807, 13749, 14509, 15381, 15705, 15959, 16583, 16761, 17163, 17473, 17787, 18813, 19283, 19831, 19937, 20483, 20513, 20633, 21673, 22121

Offset

1,1

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Mathematica

semiPrimeQ:=Last[Total[FactorInteger[#]]]==2&;
A263510=Select[Range[10000], Apply[And, Map[CompositeQ[#]&&OddQ[#]&&SquareFreeQ[#]&&(!semiPrimeQ[#])&, {6#+1, 3#+2, 6#+7}]]&]
csnQ[n_]:=Module[{c={6n+1, 3n+2, 6n+7}}, AllTrue[c, CompositeQ]&&AllTrue[ c, SquareFreeQ]&&AllTrue[c, OddQ]&&FreeQ[PrimeOmega[c], 2]]; Select[Range[ 22200], csnQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 02 2020 *)

Crossrefs

Cf. A001358, A264778, A264779.

Sequence in context: A205660 A205949 A205460 * A250970 A238035 A248485

Adjacent sequences: A263507 A263508 A263509 * A263511 A263512 A263513

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Nov 24 2015

Status

approved