

A117204


Squarefree positive integers k such that 2*k+1 is also squarefree.


5



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, 46, 47, 51, 53, 55, 57, 59, 61, 65, 66, 69, 70, 71, 74, 77, 78, 79, 82, 83, 86, 89, 91, 93, 95, 97, 101, 102, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119
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OFFSET

1,2


COMMENTS

The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987).  Amiram Eldar, Mar 02 2021


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000
Paul Erdős and Aleksandar Ivić, The distribution of values of a certain class of arithmetic functions at consecutive integers, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 4591.


FORMULA

a(n) = (A117203(n)  1)/2.


EXAMPLE

10 and 2*10 +1 = 21 are both squarefree, so 10 is in the sequence.


MATHEMATICA

sfQ[n_]:=SquareFreeQ[n]&&SquareFreeQ[2n+1]; Select [Range[200], sfQ] (* Harvey P. Dale, Mar 12 2011 *)


CROSSREFS

Cf. A005117, A117203, A117206.
Cf. A005384, A111153, A065474.
Sequence in context: A322846 A302496 A117344 * A129127 A078135 A073328
Adjacent sequences: A117201 A117202 A117203 * A117205 A117206 A117207


KEYWORD

nonn


AUTHOR

Leroy Quet, Mar 02 2006


EXTENSIONS

More terms from Jonathan Vos Post, Mar 03 2006
Corrected and extended by Harvey P. Dale, Mar 12 2011


STATUS

approved



