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A349230 Numbers k such that k and k+3 are consecutive squarefree numbers. 2
7, 23, 26, 43, 62, 74, 79, 115, 119, 134, 146, 151, 167, 170, 174, 187, 206, 223, 259, 274, 278, 287, 295, 314, 323, 331, 359, 362, 367, 374, 386, 403, 439, 458, 494, 506, 511, 523, 527, 530, 538, 566, 574, 583, 619, 623, 635, 638, 655, 674, 691, 710, 727, 734 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 0.0716601371276261... (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
7 is a term since 7 and 7 + 3 = 10 = 2*5 are squarefree, and 7 + 1 = 8 = 2^3 and 7 + 2 = 9 = 3^2 are not.
MATHEMATICA
Select[Range[750], Boole[SquareFreeQ /@ (# + {0, 1, 2, 3})] == {1, 0, 0, 1} &]
PROG
(PARI) isok(k) = issquarefree(k) && !issquarefree(k+1) && !issquarefree(k+2) && issquarefree(k+3); \\ Michel Marcus, Nov 11 2021
CROSSREFS
Sequence in context: A115023 A009228 A249438 * A031450 A031116 A044068
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 11 2021
STATUS
approved

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Last modified April 17 05:47 EDT 2024. Contains 371756 sequences. (Running on oeis4.)