A349231 Numbers k such that k and k+4 are consecutive squarefree numbers.

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

Offset

1,1

Comments

The asymptotic density of this sequence is 0.0149788175410999... (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

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

Cf. A005117, A007674, A020754, A280892, A349230.

Sequence in context: A335076 A044185 A044566 * A141944 A281437 A319051

Adjacent sequences: A349228 A349229 A349230 * A349232 A349233 A349234

Keyword

nonn

Author

Amiram Eldar, Nov 11 2021

Status

approved