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

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences that are permutations of the natural numbers

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

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 *)

Prog

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

Crossrefs

Sequence in context: A115966 A338744 A338745 * A249559 A182846 A292962

Adjacent sequences: A203599 A203600 A203601 * A203603 A203604 A203605

Keyword

nonn

Author

Reinhard Zumkeller, Jan 03 2012

Status

approved