A084789 Increasing gaps between 3-smooth numbers (lower end).

1, 4, 9, 12, 18, 36, 81, 108, 162, 256, 288, 324, 512, 576, 648, 768, 864, 1024, 1152, 1296, 1536, 1728, 2304, 2592, 3072, 3456, 4608, 5184, 6912, 9216, 10368, 13824, 20736, 27648, 41472, 82944, 165888, 196608, 221184, 262144, 294912, 331776

Offset: 1

Author

Reinhard Zumkeller, Jun 03 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003586, A061987, A084788, A084790, A084791.

Programs

Mathematica

s = {}; m = 13; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; s = Union[s]; d = Differences @ s; v = DeleteDuplicates @ FoldList[Max, d]; Map[s[[First@ Position[d, #]]] &, v] //Flatten (* Amiram Eldar, Jan 30 2020 *)

Formula

a(n) = A084790(n) - A084788(n).

a(n) = A003586(A084791(n)).