A004719 -id:A004719 - cp's OEIS frontend

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

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

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

A243063 Numbers generated by a Fibonacci-like sequence in which zeros are suppressed.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 61, 438, 499, 937, 1436, 2373, 389, 2762, 3151, 5913, 964, 6877, 7841, 14718, 22559, 37277, 59836, 97113, 156949, 25462, 182411, 27873, 21284, 49157, 7441, 56598, 6439, 6337, 12776, 19113, 31889, 512, 3241

Offset: 1

Anthony Sand, Jun 09 2014

Let x(1) = 1, x(2) = 1, then begin the sequence x(i) = no-zero(x(i-2) + x(i-1)), where the function no-zero(n) removes all zero digits from n.

The sequence behaves like a standard Fibonacci sequence until step 15, where x = no-zero(233 + 377) = no-zero(610) = 61. At step 16, x = 377 + 61 = 438. The sequence then proceeds until step 927, where x = no-zero(224 + 377) = no-zero(601) = 61. Therefore at step 928, x = 377 + 61 = 438 and the sequence repeats.

			x(3) = x(1) + x(2) = 1 + 1 = 2.
x(4) = x(2) + x(3) = 1 + 2 = 3.
x(15) = no-zero(x(13) + x(14)) = no-zero(233 + 377) = no-zero(610) = 61.
x(16) = 377 + 61 = 438.

Anthony Sand, Table of n, a(n) for n = 1..927
Index entries for linear recurrences with constant coefficients, order 912.

Cf. A000045, A004719, A242350, A243657, A243658, A306773.

noz:=proc(n) local a,t1,i,j; a:=0; t1:=convert(n,base,10); for i from 1 to nops(t1) do j:=t1[nops(t1)+1-i]; if j <> 0 then a := 10*a+j; fi; od: a; end; # A004719
t1:=[1,1]; for n from 3 to 100 do t1:=[op(t1),noz(t1[n-1]+t1[n-2])]; od: t1; # N. J. A. Sloane, Jun 11 2014

Nest[Append[#, FromDigits@ DeleteCases[IntegerDigits[Total@ #[[-2 ;; -1]] ], ?(# == 0 &)]] &, {1, 1}, 45] (* _Michael De Vlieger, Jun 27 2020 *)
nxt[{a_,b_}]:={b,FromDigits[DeleteCases[IntegerDigits[a+b],0]]}; NestList[nxt,{1,1},50][[All,1]] (* Harvey P. Dale, Sep 12 2022 *)

x(i) = no-zero(x(i-2) + x(i-1)). For example, no-zero(233 + 377) = no-zero(610) = 61.

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

A101594 Numbers with exactly two distinct decimal digits, neither of which is 0.

Original entry on oeis.org

12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 98, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131

Offset: 1

David Wasserman, Dec 07 2004

First differs from A125290 at a(83) = 131 != 123 = A101594(83). - Michael S. Branicky, Dec 13 2021

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A083985, A031955, A004719, A043537, A168046.

Subsequence of A052382, A125290.

a101594 n = a101594_list !! (n-1)
a101594_list = filter ((== 2) . a043537) a052382_list
-- Reinhard Zumkeller, Jun 18 2013

Select[Range[200], FreeQ[#, 0] && Length[Union[#]] == 2 & [IntegerDigits[#]] &] (* Paolo Xausa, May 06 2024 *)

def ok(n): s = set(str(n)); return len(s) == 2 and "0" not in s
print([k for k in range(132) if ok(k)]) # Michael S. Branicky, Dec 13 2021

A168046(a(n)) * A043537(A004719(a(n))) = 2. - Reinhard Zumkeller, Jun 18 2013

A125289 Numbers with unique nonzero digit in decimal representation.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 110, 111, 200, 202, 220, 222, 300, 303, 330, 333, 400, 404, 440, 444, 500, 505, 550, 555, 600, 606, 660, 666, 700, 707, 770, 777, 800, 808, 880, 888, 900, 909

Offset: 1

Reinhard Zumkeller, Nov 26 2006

A043537(a(n)) <= 2.
A043537(A004719(a(n))) = 1: A004719(a(n)) is a repdigit number, see A010785;
also numbers having exactly one partition into digit values of their decimal representations: A061827(a(n))=1.

Rémy Sigrist, Table of n, a(n) for n = 1..9207
Eric Weisstein's World of Mathematics, Repeating Decimal
Eric Weisstein's World of Mathematics, Repdigit

Cf. A125292.

is(n, base=10) = #Set(select(sign, digits(n, base)))==1 \\ Rémy Sigrist, Mar 28 2020

a(n,base=10) = { for (w=0, oo, if (n<=(base-1)*2^w, my (d=1+(n-1)\2^w, k=2^w+(n-1)%(2^w)); return (d*fromdigits(binary(k), base)), n -= (base-1)*2^w)) } \\ Rémy Sigrist, Mar 28 2020

A125289_list = [n for n in range(10**4) if len(set(str(n))-{'0'})==1]
# Chai Wah Wu, Jan 04 2015

from itertools import count, product, islice
def A125289_gen(): # generator of terms
    yield from (int(d+''.join(m)) for l in count(0) for d in '123456789' for m in product('0'+d,repeat=l))
A125289_list = list(islice(A125289_gen(),20)) # Chai Wah Wu, Mar 14 2025

cp's OEIS Frontend

A004722 Delete all digits 3 from the terms of 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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A243063 Numbers generated by a Fibonacci-like sequence in which zeros are suppressed.

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

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