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

Author

Amiram Eldar, Nov 11 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

Select[Range[750], Boole[SquareFreeQ /@ (# + {0, 1, 2, 3})] == {1, 0, 0, 1} &]

PARI

isok(k) = issquarefree(k) && !issquarefree(k+1) && !issquarefree(k+2) && issquarefree(k+3); \\ Michel Marcus, Nov 11 2021