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

1,3

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.

Formula

If the offset were changed to 0: a(0) = 0, a(n+1) = f(a(n)+1,f(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

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 *)

Prog

(Magma) [ n: n in [0..89] | not 2 in Intseq(n) ];  // Bruno Berselli, May 28 2011
(sh) seq 0 1000 | grep -v 2; # Joerg Arndt, May 29 2011
(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
(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

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

Sequence in context: A026511 A321153 A304814 * A298112 A026417 A026421

Adjacent sequences: A052401 A052402 A052403 * A052405 A052406 A052407

Keyword

base,easy,nonn

Author

Henry Bottomley, Mar 13 2000

Extensions

Offset changed by Reinhard Zumkeller, Oct 07 2014

Status

approved