A004722 -id:A004722 - 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

A004721 Delete all 2's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, 14, 15, 16, 17, 18, 19, 0, 1, 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, 75

Offset: 0

N. J. A. Sloane

Cf. A004719, A004720, A004722, A004723, A004724, A004725, A004726, A004727, A004728.

d[n_]:=IntegerDigits[n]; t={0}; Do[If[Union[d[n]]!={2},n=FromDigits[DeleteCases[d[n],2]]; AppendTo[t,n]],{n,75}]; t (* Jayanta Basu, May 17 2013 *)

def A004721(n):
    l = len(str(n))
    m = 2*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 1 if k == m else int(str(k).replace('2','')) # Chai Wah Wu, Apr 20 2021

A004724 Delete all 5's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 3, 36, 37, 38, 39, 40, 41, 42, 43, 44, 4, 46, 47, 48, 49, 0, 1, 2, 3, 4, 6, 7, 8, 9, 60, 61, 62, 63, 64, 6, 66, 67, 68, 69, 70, 71, 72, 73, 74, 7, 76

Offset: 0

N. J. A. Sloane

In contrast to the variant A004180 where a(n) = 0 when all the digits of n are 5's, here a number completely disappears in that case, so that subsequent indices are shifted and for n > 4, a(n) is not the result of deleting 5's from n: see formula. - M. F. Hasler, Jan 13 2020

			From  _M. F. Hasler_, Jan 13 2020: (Start)
After a(4) = 4 comes a(5) = 6, since the number 5 completely disappears.
a(48) = 49 is followed by 0, 1, 2, 3, 4 (i.e., 50, ..., 54 with the initial digit removed) and then a(54) = 6, because 55 disappears completely.
Illustration of the formula: as long as n < 5 (the first number that completely disappears) we have a(n) = A004180(n). Here n has 1 digit but n+1 does not exceed the (single repdigit) 5 (left hand side in the Iverson bracket), so m = 0. From n = 5 on, n+1 > 5, so m = 1.
Then, when n has L(n) = 2 digits, we still have n = 2 - 1 = 1 as long as n+2 <= 55 or n <= 53, but m = 3 for n > 55 - 2 = 53, i.e., from n = 54 on (where the term 55 has disappeared, see above).
Similarly, m = 3 for n > 555 - 3, i.e., from n >= 553 on, etc. (End)

Cf. A004180 (delete digits 5 in n), A052413 (numbers with no digit 5).

Cf. A004719, A004720, A004721, A004722, A004723, A004725, A004726, A004727, A004728.

m=1; for u=0:76 v=dec2base(u, 10)-'0'; v = v(v~=5);  if length(v)>0; sol(m)=(str2num(strrep(num2str(v), ' ', ''))); m=m+1; end; end; sol % Marius A. Burtea, Jan 16 2020

apply( {A004724(n,L=logint(n+!n,10)+1)=A004180(n+L-(10^L\9*5-L>=n))}, [0..99])
A004724_upto(N)={[fromdigits(v)|v<-[[d|d<-digits(n+!n*50),d!=5]|n<-[0..N]],#v]} \\ M. F. Hasler, Jan 13 2020

def A004724(n):
    l = len(str(n))
    m = 5*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 4 if k == m else int(str(k).replace('5','')) # Chai Wah Wu, Apr 20 2021

a(n) = A004180(n + m) where m = L(n) - [ (10^L(n)-1)/9*5 >= n + L(n) ], L(n) = floor(log_10(max(n,1)) + 1), the number of digits of n, and [...] is the Iverson bracket (1 if true, 0 else). - M. F. Hasler, Jan 13 2020

A004723 Delete all 4's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 15, 16, 17, 18, 19, 20, 21, 22, 23, 2, 25, 26, 27, 28, 29, 30, 31, 32, 33, 3, 35, 36, 37, 38, 39, 0, 1, 2, 3, 5, 6, 7, 8, 9, 50, 51, 52, 53, 5, 55, 56, 57, 58, 59, 60, 61, 62, 63, 6, 65, 66, 67, 68, 69, 70, 71, 72, 73, 7, 75

Offset: 0

N. J. A. Sloane

Differs from A004179 where A004179(4) = A004179(44) = A004179(444) = ... = 0. - Michel Marcus, May 17 2019

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

Cf. A004179.

Cf. A004719, A004720, A004721, A004722, A004724, A004725, A004726, A004727, A004728.

m=1;
for u=0:150
v=dec2base(u, 10)-'0'; v = v(v~=4);
  if length(v)>0;sol(m)=(str2num(strrep(num2str(v), ' ', ''))); m=m+1; end;
end;
sol % Marius A. Burtea, May 17 2019

f:= proc(n) local L,i;
  L:= subs(4=NULL, convert(n,base,10));
  if L = [] then return NULL fi;
  add(L[i]*10^(i-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, May 17 2019

def A004723(n):
    l = len(str(n))
    m = 4*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 3 if k == m else int(str(k).replace('4','')) # Chai Wah Wu, Apr 20 2021

A004725 Delete all 6's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 27, 28, 29, 30, 31, 32, 33, 34, 35, 3, 37, 38, 39, 40, 41, 42, 43, 44, 45, 4, 47, 48, 49, 50, 51, 52, 53, 54, 55, 5, 57, 58, 59, 0, 1, 2, 3, 4, 5, 7, 8, 9, 70, 71, 72, 73, 74, 75, 7

Offset: 0

N. J. A. Sloane

Cf. A004719, A004720, A004721, A004722, A004723, A004724, A004726, A004727, A004728.

d6[n_]:=Module[{c=DeleteCases[IntegerDigits[n],6]},If[c=={},Nothing, FromDigits[ c]]]; Array[d6,80,0] (* Harvey P. Dale, Oct 09 2017 *)

def A004725(n):
    l = len(str(n))
    m = 2*(10**l-1)//3
    k = n + l - int(n+l < m)
    return 5 if k == m else int(str(k).replace('6','')) # Chai Wah Wu, Apr 20 2021

A004726 Delete all 7's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2, 28, 29, 30, 31, 32, 33, 34, 35, 36, 3, 38, 39, 40, 41, 42, 43, 44, 45, 46, 4, 48, 49, 50, 51, 52, 53, 54, 55, 56, 5, 58, 59, 60, 61, 62, 63, 64, 65, 66, 6, 68, 69, 0, 1, 2

Offset: 0

N. J. A. Sloane

Cf. A004719, A004720, A004721, A004722, A004723, A004724, A004725, A004727, A004728.

Delete[Table[FromDigits[IntegerDigits[n]/.(7->Nothing)],{n,0,80}],8] (* Harvey P. Dale, Jul 13 2025 *)

def A004726(n):
    l = len(str(n))
    m = 7*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 6 if k == m else int(str(k).replace('7','')) # Chai Wah Wu, Apr 20 2021

A004727 Delete all 8's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 3, 39, 40, 41, 42, 43, 44, 45, 46, 47, 4, 49, 50, 51, 52, 53, 54, 55, 56, 57, 5, 59, 60, 61, 62, 63, 64, 65, 66, 67, 6, 69, 70, 71

Offset: 0

N. J. A. Sloane

Cf. A004719, A004720, A004721, A004722, A004723, A004724, A004725, A004726, A004728.

def A004727(n):
    l = len(str(n))
    m = 8*(10**l-1)//9
    k = n + l - int(n+l < m)
    return 7 if k == m else int(str(k).replace('8','')) # Chai Wah Wu, Apr 20 2021

A004728 Delete all 9's from the sequence of nonnegative integers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 30, 31, 32, 33, 34, 35, 36, 37, 38, 3, 40, 41, 42, 43, 44, 45, 46, 47, 48, 4, 50, 51, 52, 53, 54, 55, 56, 57, 58, 5, 60, 61, 62, 63, 64, 65, 66, 67, 68, 6, 70, 71

Offset: 0

N. J. A. Sloane

Cf. A004719, A004720, A004721, A004722, A004723, A004724, A004725, A004726, A004727.

Join[{0},Table[FromDigits[IntegerDigits[n]/.(9->Nothing)],{n,90}]/.(0-> Nothing)] (* Harvey P. Dale, Aug 10 2019 *)

def A004728(n):
    l = len(str(n))
    m = 10**l-1
    k = n + l - int(n+l < m)
    return 8 if k == m else int(str(k).replace('9','')) # Chai Wah Wu, Apr 20 2021

A004178 Omit 3's from n.

Original entry on oeis.org

0, 1, 2, 0, 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, 0, 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

Offset: 0

N. J. A. Sloane

a(n) = 0 when n = 0 or when n is a 3-repdigit (A002277). a(n) = n when it contains no 3 among its digits. - Alonso del Arte, Oct 16 2012

			a(13) = 1 because after deleting the 3 from its base 10 representation, we're left with 1.
a(14) = 14 because there are no 3s to delete.

Cf. A004722, A052405.

Table[FromDigits[DeleteCases[IntegerDigits[n], 3]], {n, 0, 74}] (* Alonso del Arte, Oct 16 2012 *)

a(n)=subst(Pol(select(k->k-3,digits(n))),'x,10) \\ Charles R Greathouse IV, Oct 16 2012

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A052405 Numbers without 3 as a digit.

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A004721 Delete all 2's from the sequence of nonnegative integers.

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A004724 Delete all 5's from the sequence of nonnegative integers.

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A004723 Delete all 4's from the sequence of nonnegative integers.

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A004725 Delete all 6's from the sequence of nonnegative integers.

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A004726 Delete all 7's from the sequence of nonnegative integers.

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A004727 Delete all 8's from the sequence of nonnegative integers.

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A004728 Delete all 9's from the sequence of nonnegative integers.

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