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%I #24 Mar 02 2021 06:00:29
%S 1,2,3,5,6,7,10,11,14,15,17,19,21,23,26,29,30,33,34,35,38,39,41,42,43,
%T 46,47,51,53,55,57,59,61,65,66,69,70,71,74,77,78,79,82,83,86,89,91,93,
%U 95,97,101,102,105,106,107,109,110,111,113,114,115,118,119
%N Squarefree positive integers k such that 2*k+1 is also squarefree.
%C The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987). - _Amiram Eldar_, Mar 02 2021
%H Ivan Neretin, <a href="/A117204/b117204.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Erdős and Aleksandar Ivić, <a href="https://users.renyi.hu/~p_erdos/1987-32b.pdf">The distribution of values of a certain class of arithmetic functions at consecutive integers</a>, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 45-91.
%F a(n) = (A117203(n) - 1)/2.
%e 10 and 2*10 +1 = 21 are both squarefree, so 10 is in the sequence.
%t sfQ[n_]:=SquareFreeQ[n]&&SquareFreeQ[2n+1]; Select [Range[200],sfQ] (* _Harvey P. Dale_, Mar 12 2011 *)
%Y Cf. A005117, A117203, A117206.
%Y Cf. A005384, A111153, A065474.
%K nonn
%O 1,2
%A _Leroy Quet_, Mar 02 2006
%E More terms from _Jonathan Vos Post_, Mar 03 2006
%E Corrected and extended by _Harvey P. Dale_, Mar 12 2011