A007417 - OEIS

A007417

If k appears, 3k does not.
(Formerly M0954)

1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 94, 95, 97, 98, 99, 100

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The characteristic function of this sequence is given byA014578.-Philippe Deléham,Mar 21 2004

Numbers whose ternary representation ends in even number of zeros. -Philippe Deléham,Mar 25 2004

Numbers for which 3 is not an infinitary divisor. -Vladimir Shevelev,Mar 18 2013

Where odd terms occur inA051064.-Reinhard Zumkeller,May 23 2013

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Iain Fox,Table of n, a(n) for n = 1..10000(first 1000 terms from T. D. Noe)

Aviezri S. Fraenkel,The vile, dopey, evil and odious game players,Discrete Math. 312 (2012), no. 1, 42-46.

S. Plouffe,Email to N. J. A. Sloane, Jun. 1994

David Wakeham and David R. Wood,On multiplicative Sidon sets,INTEGERS, 13 (2013), #A26.

Index entries for 3-automatic sequences.

FORMULA

Limit_{n->infinity} a(n)/n = 4/3. -Philippe Deléham,Mar 21 2004

Partial sums ofA092400.Indices of even numbers inA007949.Indices of odd numbers inA051064.a(n) =A092401(2n-1). -Philippe Deléham,Mar 29 2004

{a(n)} =A052330({A042948(n)}), where {a(n)} denotes the set of integers in the sequence. -Peter Munn,Aug 31 2019

EXAMPLE

FromGary W. Adamson,Mar 02 2010: (Start)

Given the following multiplication table: top row = "not multiples of 3", left column = powers of 3; we get:

...

1 2 4 5 7 8 10 11 13

3 6 12 15 21 24 30 33 39

9 18 36 45 63 72 90 99 114

27 54 108

... If rows are labeled (1, 2, 3,...) then odd-indexed rows are in the set; but evens not. Examples: 9 is in the set since 3 is not, but 27 in row 4 can't be. (End)

MATHEMATICA

Select[ Range[100], (# // IntegerDigits[#, 3]& // Split // Last // Count[#, 0]& // EvenQ)&] (*Jean-François Alcover,Mar 01 2013, afterPhilippe Deléham*)

Select[Range[100], EvenQ@ IntegerExponent[#, 3] &] (*Michael De Vlieger,Sep 01 2020 *)

PROG

(Haskell)

import Data.List (delete)

a007417 n = a007417_list!! (n-1)

a007417_list = s [1..] where

s (x:xs) = x: s (delete (3*x) xs)

(PARI) is(n) = { my(i = 0); while(n%3==0, n/=3; i++); i%2==0; } \\Iain Fox,Nov 17 2017

(PARI) is(n)=valuation(n, 3)%2==0; \\Joerg Arndt,Aug 08 2020

CROSSREFS

Complement ofA145204.-Reinhard Zumkeller,Oct 04 2008

Cf.A007949,A014578(characteristic function),A042948,A051064,A052330,A092400,A092401.