A092401 List of pairs n, 3n, where n is the least unused number so far.

1, 3, 2, 6, 4, 12, 5, 15, 7, 21, 8, 24, 9, 27, 10, 30, 11, 33, 13, 39, 14, 42, 16, 48, 17, 51, 18, 54, 19, 57, 20, 60, 22, 66, 23, 69, 25, 75, 26, 78, 28, 84, 29, 87, 31, 93, 32, 96, 34, 102, 35, 105, 36, 108, 37, 111, 38, 114, 40, 120, 41, 123, 43, 129, 44, 132, 45, 135, 46

Offset: 1

Author

Philippe Deléham, Mar 22 2004

Keywords

• easy
• nice
• nonn

Comments

A permutation of the natural numbers.

Links

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

Crossrefs

Cf. A036552, A203602 (inverse).

Programs

Haskell

import Data.List (delete)
a092401 n = a092401_list !! (n-1)
a092401_list = f [1..] where
   f (x:xs) = x : x' : f (delete x' xs) where x' = 3*x
-- Reinhard Zumkeller, Jan 03 2012

Mathematica

A007417 = Select[ Range[100], (# // IntegerDigits[#, 3]& // Split // Last // Count[#, 0]& // EvenQ)&]; a[n_] := If[ OddQ[n], A007417[[(n+1)/2]], 3*A007417[[n/2]] ]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 01 2013, from formula *)

Python

from sympy import integer_log
def A092401(n):
    def f(x): return (n+1>>1)+x-sum(((m:=x//9**i)-2)//3+(m-1)//3+2 for i in range(integer_log(x,9)[0]+1))
    m, k = n+1>>1, f(n+1>>1)
    while m != k: m, k = k, f(k)
    return m if n&1 else 3*m # Chai Wah Wu, Feb 16 2025

Formula

a(2n-1) = A007417(n), a(2n) = 3*A007417(n).