A349234 Numbers k such that k and k+3 are consecutive cubefree numbers.

79, 134, 295, 342, 350, 374, 511, 566, 623, 727, 782, 943, 998, 1159, 1214, 1430, 1591, 1623, 1646, 1807, 1862, 2023, 2078, 2239, 2294, 2374, 2399, 2455, 2510, 2623, 2671, 2726, 2887, 2942, 3086, 3103, 3158, 3319, 3374, 3428, 3535, 3590, 3623, 3751, 3806, 3967

Offset

1,1

Comments

The asymptotic density of this sequence is 0.0123046264590258... (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

79 is a term since 79 and 79 + 3 = 82 = 2*41 are cubefree, and 79 + 1 = 80 = 2^4*5 and 79 + 2 = 81 = 3^4 are not.

Mathematica

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[4000], Boole[cubeFreeQ /@ (# + Range[0, 3])] == {1, 0, 0, 1} &]
SequencePosition[Table[If[Max[FactorInteger[n][[All, 2]]]<3, 1, 0], {n, 4000}], {1, 0, 0, 1}][[All, 1]] (* Harvey P. Dale, May 08 2022 *)

Crossrefs

Cf. A004709, A046099, A340152, A349233, A349235.

Sequence in context: A142520 A140743 A262493 * A141997 A107184 A250658

Adjacent sequences: A349231 A349232 A349233 * A349235 A349236 A349237

Keyword

nonn

Author

Amiram Eldar, Nov 11 2021

Status

approved