A085240 As exponents > 0 in powers of 2 or 3 (A006899) occur in A085238 exactly twice, a self-inverse permutation of natural numbers is induced.

2, 1, 5, 7, 3, 10, 4, 12, 15, 6, 18, 8, 20, 23, 9, 25, 28, 11, 31, 13, 33, 36, 14, 38, 16, 41, 43, 17, 46, 49, 19, 51, 21, 54, 56, 22, 59, 24, 62, 64, 26, 67, 27, 69, 72, 29, 74, 77, 30, 80, 32, 82, 85, 34, 87, 35, 90, 93, 37, 95, 98, 39, 100, 40, 103, 105, 42, 108

Offset: 1

Author

Reinhard Zumkeller, Jun 22 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

Cf. A006899, A085238.

Programs

Mathematica

seq[lim_] := Module[{r2 = Range[0, Floor[Log2[lim]]], r3 = Range[0, Floor[Log[3, lim]]], s, m, v, ind, j}, s = Rest@Rest@ SortBy[Join[{#, 2^#} & /@ r2, {#, 3^#} & /@ r3], Last][[;; , 1]]; ind = Flatten /@ (Position[s, #] & /@ Range[Max[s]]); m = Max[Flatten[ind]]; v = Table[0, {m}]; Do[If[Length[i] == 2, v[[i[[1]]]] = i[[2]]; v[[i[[2]]]] = i[[1]]], {i, ind}]; TakeWhile[v, # > 0 &]]; seq[10^25] (* Amiram Eldar, Mar 25 2025 *)

Formula

A085238(n+1) = A085238(a(n)+1). [corrected by Amiram Eldar, Mar 25 2025]

a(a(n)) = n.