A052405 Numbers without 3 as a digit.

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89

Offset: 1

Author

Henry Bottomley, Mar 13 2000

Keywords

• base
• easy
• nonn

Comments

This sequence also represents the minimal number of straight lines of a covering tree to cover n X n points arranged in a symmetrical grid. - Marco Ripà, Sep 20 2018

Examples

			22 has no 3s among its digits, hence it is in the sequence.
23 has one 3 among its digits, hence it is not in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A004178, A004722, A038611 (subset of primes), A082832 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Cf. A011533 (complement).

Programs

Haskell

a052405 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 2 then r + 1 else r  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

Magma

[ n: n in [0..89] | not 3 in Intseq(n) ];  // Bruno Berselli, May 28 2011

Maple

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<3, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Mathematica

Select[Range[0, 89], DigitCount[#, 10, 3] == 0 &] (* Alonso del Arte, Oct 16 2012 *)

PARI

is(n)=n=digits(n);for(i=1,#n,if(n[i]==3,return(0)));1 \\ Charles R Greathouse IV, Oct 16 2012
apply( {A052405(n)=fromdigits(apply(d->d+(d>2),digits(n-1,9)))}, [1..99]) \\ a(n)
next_A052405(n, d=digits(n+=1))={for(i=1, #d, d[i]==3&& return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038611. \\ M. F. Hasler, Jan 11 2020

Python

from gmpy2 import digits
def A052405(n): return int(digits(n-1,9).translate(str.maketrans('345678','456789'))) # Chai Wah Wu, Jun 28 2025

sh

seq 0 1000 | grep -v 3; # Joerg Arndt, May 29 2011

Formula

a(n) >> n^k with k = log(10)/log(9) = 1.0479.... - Charles R Greathouse IV, Oct 16 2012

a(n) = replace digits d > 2 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{n>1} 1/a(n) = A082832 = 20.569877... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014