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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 (list; graph; refs; listen; history; text; internal format)
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. 45-91.

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

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)