This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A172186 #22 Feb 26 2024 01:22:18
%S A172186 1,2,5,6,10,14,21,29,30,33,34,38,41,42,46,57,61,65,66,69,70,77,78,82,
%T A172186 86,93,101,102,105,106,109,110,113,114,118,129,133,138,141,142,145,
%U A172186 154,158,165,173,177,178,182,185,186,190,194,201,205,209,210,213,214,217,218
%N A172186 Numbers k such that k, k+1 and 2*k+1 are squarefree.
%C A172186 This sequence is similar to A007674. For terms in A007674 which lack in this sequence see A172187.
%C A172186 The asymptotic density of this sequence is 2 * Product_{p prime} (1 - 3/p^2) = 2 * A206256 = 0.250973961811... (Tsang, 1985). - _Amiram Eldar_, Feb 26 2024
%H A172186 Amiram Eldar, <a href="/A172186/b172186.txt">Table of n, a(n) for n = 1..10000</a>
%H A172186 Kai-Man Tsang, <a href="https://doi.org/10.1112/S0025579300011049">The distribution of r-tuples of square-free numbers</a>, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.
%F A172186 a(n) = (A179017(n)-1)/2.
%t A172186 Select[Range[250], And @@ SquareFreeQ /@ {#, # + 1, 2 # + 1} &] (* _Harvey P. Dale_, Mar 11 2011 *)
%Y A172186 Cf. A007674, A172187, A179017, A206256.
%K A172186 nonn
%O A172186 1,2
%A A172186 _Artur Jasinski_, Jan 28 2010