A084788 Sizes of successive increasing gaps between 3-smooth numbers.

1, 2, 3, 4, 6, 12, 15, 20, 30, 32, 36, 60, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 288, 324, 384, 432, 576, 648, 864, 1152, 1296, 1728, 2592, 3456, 5184, 10368, 11259, 13344, 15012, 17792, 20016, 22518, 26688, 30024, 40032, 45036, 53376

Offset: 1

Author

Reinhard Zumkeller, Jun 03 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Smooth Number

Crossrefs

Cf. A003586, A061987, A084789, A084790, A084791.

Programs

Mathematica

s = {}; m = 13; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; DeleteDuplicates @ FoldList[Max, Differences @ Union[s]] (* Amiram Eldar, Jan 30 2020 *)
DeleteDuplicates[Differences[Select[Range[10^6],Max[FactorInteger[#][[All,1]]]<5&]],GreaterEqual] (* Harvey P. Dale, Nov 22 2022 *)

Formula

a(n) = A084790(n) - A084789(n).

a(n) = A061987(A084791(n)).