A172186 - OEIS

%I #22 Feb 26 2024 01:22:18

%S 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 86,93,101,102,105,106,109,110,113,114,118,129,133,138,141,142,145,

%U 154,158,165,173,177,178,182,185,186,190,194,201,205,209,210,213,214,217,218

%N Numbers k such that k, k+1 and 2*k+1 are squarefree.

%C This sequence is similar to A007674. For terms in A007674 which lack in this sequence see A172187.

%C 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 Amiram Eldar, <a href="/A172186/b172186.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n) = (A179017(n)-1)/2.

%t Select[Range[250], And @@ SquareFreeQ /@ {#, # + 1, 2 # + 1} &]  (* _Harvey P. Dale_, Mar 11 2011 *)

%Y Cf. A007674, A172187, A179017, A206256.

%K nonn

%O 1,2

%A _Artur Jasinski_, Jan 28 2010