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 A052383 Numbers without 1 as a digit. 27
 0, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020 FORMULA a(1) = 1, a(n + 1) = f(a(n) + 1, a(n) + 1) where f(x, y) = if x < 10 and x <> 1 then y else if x mod 10 = 1 then f(y + 1, y + 1) else f(floor(x/10), y). - Reinhard Zumkeller, Mar 02 2008 a(n) is the replacement of all nonzero digits d by d + 1 in the base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014 Sum_{k>1} 1/a(k) = A082830 = 16.176969... (Kempner series). - Bernard Schott, Jan 12 2020 MAPLE M:= 3: # to get all terms with up to M digits B:= {\$2..9}: A:= B union {0}: for m from 1 to M do B:= map(b -> seq(10*b+j, j={0, \$2..9}), B); A:= A union B; od: sort(convert(A, list)); # Robert Israel, Jan 11 2016 # second program: A052383 := proc(n)       option remember;       if n = 1 then         0;     else         for a from procname(n-1)+1 do             if nops(convert(convert(a, base, 10), set) intersect {1}) = 0 then                 return a;             end if;         end do:     end if; end proc: # R. J. Mathar, Jul 31 2016 # third Maple program: a:= proc(n) local l, m; l, m:= 0, n-1;       while m>0 do l:= (d->         `if`(d=0, 0, 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 ban1Q[n_] := FreeQ[IntegerDigits[n], 1] == True; Select[Range[0, 89], ban1Q[#] &] (* Jayanta Basu, May 17 2013 *) Select[Range[0, 99], DigitCount[#, 10, 1] == 0 &] (* Alonso del Arte, Jan 12 2020 *) PROG (MAGMA) [ n: n in [0..89] | not 1 in Intseq(n) ];  // Bruno Berselli, May 28 2011 (sh) seq 0 1000 | grep -v 1; # Joerg Arndt, May 29 2011 (PARI) a(n)=my(v=digits(n, 9)); for(i=1, #v, if(v[i], v[i]++)); subst(Pol(v), 'x, 10) \\ Charles R Greathouse IV, Oct 04 2012 (PARI) apply( {A052383(n)=fromdigits(apply(d->d+!!d, digits(n-1, 9)))}, [1..99]) \\ Defines the function and computes it for indices 1..99 (check & illustration) select( {is_A052383(n)=!setsearch(Set(digits(n)), 1)}, [0..99]) \\ Define the characteristic function is_A; as illustration, select the terms in [0..99] next_A052383(n, d=digits(n+=1))={for(i=1, #d, d[i]==1&& return((1+n\d=10^(#d-i))*d)); n} \\ Successor function: efficiently skip to the next a(k) > n. Used in A038603.  - M. F. Hasler, Jan 11 2020 (Haskell) a052383 = f . subtract 1 where    f 0 = 0    f v = 10 * f w + if r > 0 then r + 1 else 0  where (w, r) = divMod v 9 -- Reinhard Zumkeller, Oct 07 2014 (Scala) (0 to 99).filter(_.toString.indexOf('1') == -1) // Alonso del Arte, Jan 12 2020 CROSSREFS Cf. A004176, A004720, A011531 (complement), A038603 (subset of primes), A082830 (Kempner series), A248518, A248519. Cf. A052382 (without 0), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9). Sequence in context: A140281 A039077 A247803 * A110803 A109795 A248500 Adjacent sequences:  A052380 A052381 A052382 * A052384 A052385 A052386 KEYWORD base,easy,nonn AUTHOR Henry Bottomley, Mar 13 2000 EXTENSIONS Offset changed by Reinhard Zumkeller, Oct 07 2014 STATUS approved

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Last modified January 16 22:45 EST 2021. Contains 340213 sequences. (Running on oeis4.)