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A349231 Numbers k such that k and k+4 are consecutive squarefree numbers. 2
47, 97, 123, 341, 349, 422, 474, 547, 602, 723, 773, 1023, 1249, 1273, 1322, 1374, 1419, 1447, 1518, 1663, 1673, 1847, 1861, 1923, 2006, 2022, 2055, 2105, 2149, 2222, 2274, 2347, 2365, 2522, 2526, 2573, 2643, 2823, 2870, 3049, 3122, 3183, 3210, 3247, 3282, 3427 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 0.0149788175410999... (Mossinghoff et al., 2021).
LINKS
Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, The distribution of k-free numbers, Mathematics of Computation, Vol. 90, No. 328 (2021), pp. 907-929; arXiv preprint, arXiv:1912.04972 [math.NT], 2019-2020.
EXAMPLE
47 is a term since 47 and 47 + 4 = 51 = 3*17 are squarefree, and 47 + 1 = 48 = 2^4*3, 47 + 2 = 49 = 7^2 and 47 + 3 = 50 = 2*5^2 are not.
MATHEMATICA
Select[Range[3500], Boole[SquareFreeQ /@ (# + Range[0, 4])] == {1, 0, 0, 0, 1} &]
CROSSREFS
Sequence in context: A335076 A044185 A044566 * A141944 A281437 A319051
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 11 2021
STATUS
approved

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Last modified April 21 07:37 EDT 2024. Contains 371850 sequences. (Running on oeis4.)