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

1,1

Links

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

Index entries for sequences that are permutations of the natural numbers.

Formula

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

a(a(n)) = n.

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 *)

Crossrefs

Cf. A006899, A085238.

Sequence in context: A392058 A332022 A109261 * A002251 A093545 A293845

Adjacent sequences: A085237 A085238 A085239 * A085241 A085242 A085243

Keyword

nonn

Author

Reinhard Zumkeller, Jun 22 2003

Status

approved