A052404 Numbers without 2 as a digit.

0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88, 89

Offset: 1

Author

Henry Bottomley, Mar 13 2000

Keywords

• base
• easy
• nonn

References

• M. J. Halm, Word Weirdness, Mpossibilities 66 (Feb. 1998), p. 5.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• M. J. Halm, Games
• M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A004177, A004721, A072809, A082831 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

See A038604 for the subset of primes. - M. F. Hasler, Jan 11 2020

Programs

Haskell

a052404 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 1 then r + 1 else r  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

Magma

[ n: n in [0..89] | not 2 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<2, 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

ban2Q[n_]:=FreeQ[IntegerDigits[n],2]==True; Select[Range[0,89],ban2Q[#] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0,100],DigitCount[#,10,2]==0&] (* Harvey P. Dale, Apr 13 2015 *)

PARI

lista(nn, d=2) = {for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8),d), print1(n, ", ")););} \\ Michel Marcus, Feb 21 2015

PARI

apply( {A052404(n)=fromdigits(apply(d->d+(d>1),digits(n-1,9)))}, [1..99])
next_A052404(n, d=digits(n+=1))={for(i=1, #d, d[i]==2&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n: if there's a digit 2 in n+1, replace the first occurrence by 3 and all following digits by 0.
(A052404_vec(N)=vector(N, i, N=if(i>1, next_A052404(N))))(99) \\ first N terms
select( {is_A052404(n)=!setsearch(Set(digits(n)),2)}, [0..99])
(A052404_upto(N)=select( is_A052404, [0..N]))(99) \\ M. F. Hasler, Jan 11 2020

Python

from gmpy2 import digits
def A052404(n): return int(''.join(str(int(d)+1) if d>'1' else d for d in digits(n-1,9))) # Chai Wah Wu, Aug 30 2024

sh

seq 0 1000 | grep -v 2; # Joerg Arndt, May 29 2011

Formula

If the offset were changed to 0: a(0) = 0, a(n+1) = f(a(n)+1,a(n)+1) where f(x,y) = if x<10 and x<>2 then y else if x mod 10 = 2 then f(y+1,y+1) else f(floor(x/10),y). - Reinhard Zumkeller, Mar 02 2008

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

Sum_{k>1} 1/a(k) = A082831 = 19.257356... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014