A349230 Numbers k such that k and k+3 are consecutive squarefree numbers.

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

Offset

1,1

Comments

The asymptotic density of this sequence is 0.0716601371276261... (Mossinghoff et al., 2021).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A005117, A007674, A020754, A280892, A349231.

Sequence in context: A115023 A009228 A249438 * A031450 A031116 A044068

Adjacent sequences: A349227 A349228 A349229 * A349231 A349232 A349233

Keyword

nonn

Author

Amiram Eldar, Nov 11 2021

Status

approved