A084791 Where record gaps between 3-smooth numbers occur.

1, 4, 7, 8, 10, 14, 19, 21, 24, 28, 29, 30, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 50, 51, 53, 54, 58, 59, 63, 67, 68, 72, 78, 82, 88, 99, 110, 113, 115, 118, 120, 122, 125, 127, 133, 135, 138, 140, 146, 148, 154, 160, 162, 168, 175, 176, 177, 183, 190, 191, 192

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, A084788, A084789, A084790.

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[First@ Position[d, #] &, v] //Flatten (* Amiram Eldar, Jan 30 2020 *)
Module[{nn=10^7,ts},ts=Select[Range[nn],Max[FactorInteger[#][[;;,1]]]<5&];DeleteDuplicates[Thread[{Range[Length[ts]-1],Differences[ts]}],GreaterEqual[#1[[2]],#2[[2]]]&]][[;;,1]] (* The program generates the first 58 terms of the sequence. *) (* Harvey P. Dale, Aug 11 2025 *)

Formula

A084788(n) = A061987(a(n)).

A084789(n) = A003586(a(n)).

A084790(n) = A003586(a(n) + 1).