A203602 Inverse permutation to A092401.

1, 3, 2, 5, 7, 4, 9, 11, 13, 15, 17, 6, 19, 21, 8, 23, 25, 27, 29, 31, 10, 33, 35, 12, 37, 39, 14, 41, 43, 16, 45, 47, 18, 49, 51, 53, 55, 57, 20, 59, 61, 22, 63, 65, 67, 69, 71, 24, 73, 75, 26, 77, 79, 28, 81, 83, 30, 85, 87, 32, 89, 91, 93, 95, 97, 34, 99

Offset: 1

Author

Reinhard Zumkeller, Jan 03 2012

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences that are permutations of the natural numbers

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (mapMaybe)
a203602 n = a203602_list !! (n-1)
a203602_list = map (+ 1) $ mapMaybe (`elemIndex` a092401_list) [1..]

Mathematica

div[n_, m_]=Floor[n/m // Chop]-Ceiling[n/m // Chop](*n not divisible by m=>-1, else 0*); ind[m_]:=Sum[(-1)^(n) div[m, 3^n], {n, 1, Floor[Log[m]/Log[3] // FullSimplify]}] + Mod[Floor[Log[3 m]/Log[3] // FullSimplify], 2];(* returns 0 or 1 depending on if we have an 'n' term (=>1) or a '3n' term (=>0) *) f[m_] := (2* Sum[(-1)^(n) Floor[m/(3^(n)) // FullSimplify], {n, 0, Floor[Log[m]/Log[3] // FullSimplify]}] - 1)* ind[m] + (1 - ind[m]) (2* Sum[(-1)^(n) Floor[m/(3^(n + 1)) // FullSimplify], {n, 0, -1 + Floor[Log[m]/Log[3] // FullSimplify]}]);
Table[f[k], {k, 1, 50}] (* Daniel Hoying, Aug 06 2020 *)

Formula

a(n) = -2*(Sum_{k=0..-1+floor(log(n)/log(3))} (-1)^k*floor(n/3^(k+1)))*(-1 + (floor(log(3*n)/log(3)) mod 2)+Sum_{k=1..floor(log(n)/log(3))} (-1)^k*(-ceiling(n/3^k) + floor(n/3^k))) + (-1 + 2*Sum_{k=0..floor(log(n)/log(3))} (-1)^k*floor(n/3^k))*((floor(log(3*n)/log(3)) mod 2)+Sum_{k=1..floor(log(n)/log(3))} (-1)^k*(-ceiling(n/3^k) + floor(n/3^k))). - Daniel Hoying, Aug 06 2020