A004724 -id:A004724 - cp's OEIS frontend

A052413 Numbers without 5 as a digit.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

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. A004180, A004724, A038613 (subset of primes), A082834 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

a052413 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 4 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 5 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<5, 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[100],!MemberQ[IntegerDigits[#],5]&] (* Harvey P. Dale, Feb 20 2013 *)

apply( {A052413(n)=fromdigits(apply(d->d+(d>4),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052413(n)=!setsearch(Set(digits(n)),5)}, [0..99]) \\ used in A038613
next_A052413(n, d=digits(n+=1))={for(i=1,#d, d[i]==5&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n; used in A038613. - M. F. Hasler, Jan 11 2020

# see the OEIS wiki page (cf. LINKS) for more programs
def A052413(n): n-=1; return sum(n//9**e%9*6//5*10**e for e in range(math.ceil(math.log(n+1,9)))) # M. F. Hasler, Jan 13 2020

from gmpy2 import digits
def A052413(n): return int(digits(n-1,9).translate(str.maketrans('5678','6789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 5; # Joerg Arndt, May 29 2011

a(n) = replace digits d > 4 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(n) = A082834 = 21.8346008... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 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

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

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

A004180 Omit 5's from n.

Original entry on oeis.org

0, 1, 2, 3, 4, 0, 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, 0, 6, 7, 8, 9, 60, 61, 62, 63, 64, 6, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 0

N. J. A. Sloane

See A004724 for a variant where a(n) disappears when n has only digits 5. - M. F. Hasler, Jan 13 2020

Cf. A004724.

for u=0:74 ; v=dec2base(u, 10)-'0'; v = v(v~=5); if length(v)>0; sol(u+1)=(str2num(strrep(num2str(v), ' ', ''))); else; sol(u+1)=0; end; end; sol % Marius A. Burtea, Jan 13 2020

Table[FromDigits[DeleteCases[IntegerDigits[n], 5]], {n, 0, 79}] (* Harvey P. Dale, Jan 20 2015 *)

a(n)=subst(Pol(select(k->k-5,digits(n))),'x,10) \\ Charles R Greathouse IV, Oct 16 2012

A004180(n)=fromdigits([d|d<-digits(n),d!=5]) \\ M. F. Hasler, Jan 13 2020

(0 to 99).map(n => try {
  Integer.parseInt(Integer.toString(n).replace("5", ""))
} catch {
  case _: NumberFormatException => 0
}) // Alonso del Arte, Jan 13 2020

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A052413 Numbers without 5 as a digit.

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

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A004722 Delete all digits 3 from the terms of 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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