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
Keywords
Examples
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.
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.
Programs
-
Mathematica
Select[Range[3500], Boole[SquareFreeQ /@ (# + Range[0, 4])] == {1, 0, 0, 0, 1} &]
Comments