A004178 -id:A004178 - cp's OEIS frontend

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

Henry Bottomley, Mar 13 2000

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

			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.

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.

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).

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

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

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

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

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

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

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

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

Offset changed by Reinhard Zumkeller, Oct 07 2014

A004722 Delete all digits 3 from the terms of the sequence of nonnegative integers.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Very similar to A004178, except that 3-repdigits (A002277) are completely removed from the sequence, whereas A004178 has 0's in their place. It is thus guaranteed that a(n) = n only when n < 3. - Alonso del Arte, Oct 18 2012

Alonso del Arte, Table of n, a(n) for n = 0..9999

Cf. A004719, A004720, A004721, A004723, A004724, A004725, A004726, A004727, A004728.

m=1;
for u=0:1000
    v=dec2base(u,10)-'0'; v = v(v~=3);
    if length(v)>0;sol(m)=(str2num(strrep(num2str(v), ' ', ''))); m=m+1; end;
end
sol % Marius A. Burtea, May 07 2019

endAt = 103; Delete[Table[FromDigits[DeleteCases[IntegerDigits[n], 3]], {n, 0, endAt}], Table[{(10^expo - 1)/3 + 1}, {expo, Floor[Log[10, endAt]]}]] (* Alonso del Arte, Apr 29 2019 *)

def A004722(n):
    l = len(str(n))
    m = (10**l-1)//3
    k = n + l - int(n+l < m)
    return 2 if k == m else int(str(k).replace('3','')) # Chai Wah Wu, Apr 20 2021

a(n) = n for -1 < n < 3;
a(n) = A004178(n + 1) for 2 < n < 32,
a(n) = A004178(n + 2) for 31 < n < 331,
a(n) = A004178(n + 3) for 330 < n < 3330,
a(n) = A004178(n + 4) for 3329 < n < 33329, etc. - Alonso del Arte, Oct 21 2012

Sean A. Irvine pointed out erroneous terms in b-file and confirmed correction, Apr 28 2019

Name edited by Felix Fröhlich, Apr 29 2019

A004177 Omit 2's from n.

Original entry on oeis.org

0, 1, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 0, 1, 0, 3, 4, 5, 6, 7, 8, 9, 30, 31, 3, 33, 34, 35, 36, 37, 38, 39, 40, 41, 4, 43, 44, 45, 46, 47, 48, 49, 50, 51, 5, 53, 54, 55, 56, 57, 58, 59, 60, 61, 6, 63, 64, 65, 66, 67, 68, 69, 70, 71, 7, 73, 74

Offset: 0

N. J. A. Sloane

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A004176, A004178, A004179, A004180, A004181, A004182, A004183, A004184.

Cf. A004719.

f:= proc(n) local L,i;
     L:= subs(2=NULL,convert(n,base,10));
     add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Sep 15 2024

Table[FromDigits[DeleteCases[IntegerDigits[n],2]],{n,0,80}] (* Harvey P. Dale, Feb 12 2022 *)

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A052405 Numbers without 3 as a digit.

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A004722 Delete all digits 3 from the terms of the sequence of nonnegative integers.

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A004177 Omit 2's from n.

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Maple

Mathematica