A052406 Numbers without 4 as a digit.

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

1,3

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.

Eric Weisstein's World of Mathematics, Uban Number

Wikipedia, Tetraphobia.

Index entries for 10-automatic sequences.

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

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 *)

Prog

(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
(Magma) [ n: n in [0..89] | not 4 in Intseq(n) ]; // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 4; # Joerg Arndt, May 29 2011
(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
(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

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).

Sequence in context: A258022 A333638 A089590 * A022306 A183298 A382717

Adjacent sequences: A052403 A052404 A052405 * A052407 A052408 A052409

Keyword

base,easy,nonn

Author

Henry Bottomley, Mar 13 2000

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

Status

approved