cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A052406 Numbers without 4 as a digit.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89
Offset: 1

Views

Author

Henry Bottomley, Mar 13 2000

Keywords

Comments

This is a frequent sequence on Chinese, Japanese and Korean elevator buttons. - Jean-Sebastien Girard (circeus(AT)hotmail.com), Jul 28 2008
Essentially numbers in base 9 (using digits 0, 1, 2, 3, 5, 6, 7, 8, 9 rather than 0-8). - Charles R Greathouse IV, Oct 13 2013

Links

Crossrefs

Cf. A004179, A004723, A011760, A038612 (subset of primes), A082833 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Programs

  • Haskell
    a052406 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 3 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014
  • Magma
    [ n: n in [0..89] | not 4 in Intseq(n) ]; // Bruno Berselli, May 28 2011
  • Maple
    a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<4, 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
  • Mathematica
    Select[Range[100], DigitCount[#, 10, 4] == 0 &] (* Alonso del Arte, Oct 13 2013 *)
  • PARI
    g(n)= local(x,v,j,flag); for(x=1,n, v=Vec(Str(x)); flag=1; for(j=1,length(v), if(v[j]=="4",flag=0)); if(flag,print1(x",") ) ) \\ Cino Hilliard, Apr 01 2007
  • PARI
    apply( {A052406(n)=fromdigits(apply(d->d+(d>3),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052406(n)=!setsearch(Set(digits(n)),4)}, [0..99]) \\ Used in A038612
next_A052406(n, d=digits(n+=1))={for(i=1, #d, d[i]!=4|| return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used for A038612. - M. F. Hasler, Jan 11 2020
  • Python
    def A052406(n): n-=1; return sum((d+(d>3))*10**i for d,i in ((n//9**i%9,i) for i in range(math.ceil(math.log(n+1,9))))) # M. F. Hasler, Jan 13 2020
  • Python
    from gmpy2 import digits
def A052406(n): return int(digits(n-1,9).translate(str.maketrans('45678','56789'))) # Chai Wah Wu, Jun 28 2025
  • sh
    seq 0 1000 | grep -v 4; # Joerg Arndt, May 29 2011

Formula

a(n) = replace digits d > 3 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{k>1} 1/a(k) = A082833 = 21.327465... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

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

Views

Author

N. J. A. Sloane

Keywords

Comments

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

Links

Crossrefs

Cf. A004179.
Cf. A004719, A004720, A004721, A004722, A004724, A004725, A004726, A004727, A004728.

Programs

  • MATLAB
    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
  • Maple
    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
  • Python
    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

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A004176, A004178, A004179, A004180, A004181, A004182, A004183, A004184.
Cf. A004719.

Programs

  • Maple
    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
  • Mathematica
    Table[FromDigits[DeleteCases[IntegerDigits[n],2]],{n,0,80}] (* Harvey P. Dale, Feb 12 2022 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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