A004180 -id:A004180 - 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

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

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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A052413 Numbers without 5 as a digit.

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

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A004177 Omit 2's from n.

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