A052414 Numbers without 6 as a digit.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89

Offset: 1

Author

Henry Bottomley, Mar 13 2000

Keywords

• base
• easy
• nonn

Links

• 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.

Crossrefs

Cf. A004181, A004725, A038614 (subset of primes), A082835 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052419 (without 7), A052421 (without 8), A007095 (without 9).

Programs

Haskell

a052414 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 5 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

Magma

[ n: n in [0..89] | not 6 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<6, 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[0,100],DigitCount[#,10,6]==0&] (* Harvey P. Dale, Jun 20 2013 *)

PARI

lista(nn)=for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8), 6), print1(n, ", "));); \\ Michel Marcus, Feb 22 2015

PARI

/* See OEIS wiki page (cf. LINKS) for more programs */
apply( {A052414(n)=fromdigits(apply(d->d+(d>5),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052414(n)=!setsearch(Set(digits(n)),6)}, [0..99]) \\ used in A038614
next_A052414(n, d=digits(n+=1))={for(i=1,#d, d[i]==6&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n, used in A038614. - M. F. Hasler, Jan 11 2020

Python

from gmpy2 import digits
def A052414(n): return int(digits(n-1,9).translate(str.maketrans('678','789'))) # Chai Wah Wu, Jun 28 2025

sh

seq 0 1000 | grep -v 6; # Joerg Arndt, May 29 2011

Formula

a(n) = replace digits d > 5 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(k) = A082835 = 22.205598... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014