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%I #73 May 05 2023 16:22:41
%S 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,
%T 39,40,41,43,44,45,46,47,48,49,50,51,53,54,55,56,57,58,59,60,61,63,64,
%U 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,83,84,85,86,87,88,89
%N Numbers without 2 as a digit.
%D M. J. Halm, Word Weirdness, Mpossibilities 66 (Feb. 1998), p. 5.
%H Reinhard Zumkeller, <a href="/A052404/b052404.txt">Table of n, a(n) for n = 1..10000</a>
%H M. J. Halm, <a href="http://michaelhalm.tripod.com/id76.htm">Games</a>
%H M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS Wiki, Jan 12 2020.
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F 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
%F a(n) = replace digits d > 1 by d + 1 in base-9 representation of n - 1. - _Reinhard Zumkeller_, Oct 07 2014
%F Sum_{k>1} 1/a(k) = A082831 = 19.257356... (Kempner series). - _Bernard Schott_, Jan 12 2020, edited by _M. F. Hasler_, Jan 14 2020
%p a:= proc(n) local l, m; l, m:= 0, n-1;
%p while m>0 do l:= (d->
%p `if`(d<2, d, d+1))(irem(m, 9, 'm')), l
%p od; parse(cat(l))/10
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Aug 01 2016
%t ban2Q[n_]:=FreeQ[IntegerDigits[n],2]==True; Select[Range[0,89],ban2Q[#] &] (* _Jayanta Basu_, May 17 2013 *)
%t Select[Range[0,100],DigitCount[#,10,2]==0&] (* _Harvey P. Dale_, Apr 13 2015 *)
%o (Magma) [ n: n in [0..89] | not 2 in Intseq(n) ]; // _Bruno Berselli_, May 28 2011
%o (sh) seq 0 1000 | grep -v 2; # _Joerg Arndt_, May 29 2011
%o (Haskell)
%o a052404 = f . subtract 1 where
%o f 0 = 0
%o f v = 10 * f w + if r > 1 then r + 1 else r where (w, r) = divMod v 9
%o -- _Reinhard Zumkeller_, Oct 07 2014
%o (PARI) lista(nn, d=2) = {for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8),d), print1(n, ", ")););} \\ _Michel Marcus_, Feb 21 2015
%o (PARI)
%o apply( {A052404(n)=fromdigits(apply(d->d+(d>1),digits(n-1,9)))}, [1..99])
%o 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.
%o (A052404_vec(N)=vector(N, i, N=if(i>1, next_A052404(N))))(99) \\ first N terms
%o select( {is_A052404(n)=!setsearch(Set(digits(n)),2)}, [0..99])
%o (A052404_upto(N)=select( is_A052404, [0..N]))(99) \\ _M. F. Hasler_, Jan 11 2020
%Y Cf. A004177, A004721, A072809, A082831 (Kempner series).
%Y 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).
%Y See A038604 for the subset of primes. - _M. F. Hasler_, Jan 11 2020
%K base,easy,nonn
%O 1,3
%A _Henry Bottomley_, Mar 13 2000
%E Offset changed by _Reinhard Zumkeller_, Oct 07 2014
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