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A052404
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Numbers without 2 as a digit.
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14
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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REFERENCES
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M. J. Halm, Word Weirdness, Mpossibilities 66 (Feb. 1998), p. 5.
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
(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])
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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