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A052405 Numbers without 3 as a digit.

%I A052405 #54 Jun 28 2025 15:43:32
%S A052405 0,1,2,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,24,25,26,27,28,
%T A052405 29,40,41,42,44,45,46,47,48,49,50,51,52,54,55,56,57,58,59,60,61,62,64,
%U A052405 65,66,67,68,69,70,71,72,74,75,76,77,78,79,80,81,82,84,85,86,87,88,89
%N A052405 Numbers without 3 as a digit.
%C A052405 This sequence also represents the minimal number of straight lines of a covering tree to cover n X n points arranged in a symmetrical grid. - _Marco Ripà_, Sep 20 2018
%H A052405 Reinhard Zumkeller, <a href="/A052405/b052405.txt">Table of n, a(n) for n = 1..10000</a>
%H A052405 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a>, OEIS Wiki, Jan 12 2020.
%H A052405 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A052405 a(n) >> n^k with k = log(10)/log(9) = 1.0479.... - _Charles R Greathouse IV_, Oct 16 2012
%F A052405 a(n) = replace digits d > 2 by d + 1 in base-9 representation of n - 1. - _Reinhard Zumkeller_, Oct 07 2014
%F A052405 Sum_{n>1} 1/a(n) = A082832 = 20.569877... (Kempner series). - _Bernard Schott_, Jan 12 2020, edited by _M. F. Hasler_, Jan 14 2020
%e A052405 22 has no 3s among its digits, hence it is in the sequence.
%e A052405 23 has one 3 among its digits, hence it is not in the sequence.
%p A052405 a:= proc(n) local l, m; l, m:= 0, n-1;
%p A052405       while m>0 do l:= (d->
%p A052405         `if`(d<3, d, d+1))(irem(m, 9, 'm')), l
%p A052405       od; parse(cat(l))/10
%p A052405     end:
%p A052405 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 01 2016
%t A052405 Select[Range[0, 89], DigitCount[#, 10, 3] == 0 &] (* _Alonso del Arte_, Oct 16 2012 *)
%o A052405 (Magma) [ n: n in [0..89] | not 3 in Intseq(n) ];  // _Bruno Berselli_, May 28 2011
%o A052405 (sh) seq 0 1000 | grep -v 3; # _Joerg Arndt_, May 29 2011
%o A052405 (PARI)
%o A052405 is(n)=n=digits(n);for(i=1,#n,if(n[i]==3,return(0)));1 \\ _Charles R Greathouse IV_, Oct 16 2012
%o A052405 apply( {A052405(n)=fromdigits(apply(d->d+(d>2),digits(n-1,9)))}, [1..99]) \\ a(n)
%o A052405 next_A052405(n, d=digits(n+=1))={for(i=1, #d, d[i]==3&& return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038611. \\ _M. F. Hasler_, Jan 11 2020
%o A052405 (Haskell)
%o A052405 a052405 = f . subtract 1 where
%o A052405    f 0 = 0
%o A052405    f v = 10 * f w + if r > 2 then r + 1 else r  where (w, r) = divMod v 9
%o A052405 -- _Reinhard Zumkeller_, Oct 07 2014
%o A052405 (Python)
%o A052405 from gmpy2 import digits
%o A052405 def A052405(n): return int(digits(n-1,9).translate(str.maketrans('345678','456789'))) # _Chai Wah Wu_, Jun 28 2025
%Y A052405 Cf. A004178, A004722, A038611 (subset of primes), A082832 (Kempner series).
%Y A052405 Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
%Y A052405 Cf. A011533 (complement).
%K A052405 base,easy,nonn
%O A052405 1,3
%A A052405 _Henry Bottomley_, Mar 13 2000
%E A052405 Offset changed by _Reinhard Zumkeller_, Oct 07 2014