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A052419 Numbers without 7 as a digit.

%I A052419 #43 Jun 28 2025 15:43:17
%S A052419 0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,28,
%T A052419 29,30,31,32,33,34,35,36,38,39,40,41,42,43,44,45,46,48,49,50,51,52,53,
%U A052419 54,55,56,58,59,60,61,62,63,64,65,66,68,69,80,81,82,83,84,85,86,88,89
%N A052419 Numbers without 7 as a digit.
%H A052419 Reinhard Zumkeller, <a href="/A052419/b052419.txt">Table of n, a(n) for n = 1..10000</a>
%H A052419 M. F. Hasler, <a href="/wiki/Numbers_avoiding_certain_digits">Numbers avoiding certain digits</a> OEIS wiki, Jan 12 2020.
%H A052419 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A052419 a(n) = replace digits d > 6 by d + 1 in base-9 representation of n - 1. - _Reinhard Zumkeller_, Oct 07 2014
%F A052419 Sum_{n>1} 1/a(n) = A082836 = 22.493475... (Kempner series). - _Bernard Schott_, Jan 12 2020, edited by _M. F. Hasler_, Jan 13 2020
%p A052419 a:= proc(n) local l, m; l, m:= 0, n-1;
%p A052419       while m>0 do l:= (d->
%p A052419         `if`(d<7, d, d+1))(irem(m, 9, 'm')), l
%p A052419       od; parse(cat(l))/10
%p A052419     end:
%p A052419 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 01 2016
%t A052419 Select[Range[100],DigitCount[#,10,7]==0&] (* _Harvey P. Dale_, Aug 23 2011 *)
%o A052419 (Magma) [ n: n in [0..89] | not 7 in Intseq(n) ]; // _Bruno Berselli_, May 28 2011
%o A052419 (sh) seq 0 1000 | grep -v 7; # _Joerg Arndt_, May 29 2011
%o A052419 (Haskell)
%o A052419 a052419 = f . subtract 1 where
%o A052419 f 0 = 0
%o A052419 f v = 10 * f w + if r > 6 then r + 1 else r where (w, r) = divMod v 9
%o A052419 -- _Reinhard Zumkeller_, Oct 07 2014
%o A052419 (PARI) lista(nn)=for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8), 7), print1(n, ", "));); \\ _Michel Marcus_, Feb 22 2015
%o A052419 (PARI) /* See OEIS wiki page for more programs. */
%o A052419 apply( {A052419(n)=fromdigits(apply(d->d+(d>6),digits(n-1,9)))}, [1..99]) \\ a(n)
%o A052419 select( {is_A052419(n)=!setsearch(Set(digits(n)),7)}, [0..99]) \\ used in A038615
%o A052419 next_A052419(n, d=digits(n+=1))={for(i=1,#d, d[i]==7&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038615. - _M. F. Hasler_, Jan 11 2020
%o A052419 (Python)
%o A052419 from gmpy2 import digits
%o A052419 def A052419(n): return int(digits(n-1,9).replace('8','9').replace('7','8')) # _Chai Wah Wu_, Jun 28 2025
%Y A052419 Cf. A004182, A004726, A038615 (subset of primes), A082836 (Kempner series).
%Y A052419 Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052421 (without 8), A007095 (without 9).
%K A052419 base,easy,nonn
%O A052419 1,3
%A A052419 _Henry Bottomley_, Mar 13 2000
%E A052419 Offset changed by _Reinhard Zumkeller_, Oct 07 2014