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A259236 Increasing sequence of numbers n such that the digits of n appear as a substring of the concatenation of the terms < n of the sequence, which is seeded with 1..9.

%I A259236 #13 Jul 16 2015 18:34:32
%S A259236 1,2,3,4,5,6,7,8,9,12,23,34,45,56,67,78,89,91,99,122,123,199,212,221,
%T A259236 222,223,231,232,233,234,312,319,322,323,332,333,334,343,344,345,431,
%U A259236 433,434,443,444,445,454,455,456,543,544,545,554,555,556,565,566,567,654,655,656,665,666,667,676,677,678,765,766,767,776,777
%N A259236 Increasing sequence of numbers n such that the digits of n appear as a substring of the concatenation of the terms < n of the sequence, which is seeded with 1..9.
%C A259236 In A048991, n is excluded if it appears in the concatenation of all earlier terms. This sequence applies the opposite criterion and excludes n if it does NOT appear in the concatenation of all earlier terms. For example, the sequences starts with 1, 2, 3, ..., therefore 12, 23 and 123 appear in the sequence, but 10, 11 and 14 do not.
%H A259236 Anthony Sand, <a href="/A259236/b259236.txt">Table of n, a(n) for n = 1..1000</a>
%F A259236 digits(n,i=1,j) = substring(sequence,i=1,j))
%e A259236 The digits of 12 appear earlier in the sequence (1, 2...), therefore 12 is included.
%e A259236 The digits of 11 do not appear earlier in the sequence, therefore 11 is excluded.
%p A259236 M:= 4: # to get all terms with <= M digits
%p A259236 with(StringTools):
%p A259236 S:= "123456789":
%p A259236 nS:= length(S):
%p A259236 Substrings:= {seq(seq(SubString(S,a..b),b=a+1..min(9,a+M-1)),a=1..8)}:
%p A259236 Cands:= map(parse,Substrings):
%p A259236 for n from 1 to 9 do A[n]:= n od:
%p A259236 for n from 10 while Cands <> {} do
%p A259236   m:= min(Cands);
%p A259236   A[n]:= m;
%p A259236   S:= cat(S,convert(m,string));
%p A259236   nm:= length(m);
%p A259236   newSubstrings:= {seq(seq(SubString(S,a..b), b = a+nm-1..min(nS+nm, a+M-1)),a=1+nS-M .. nS)};
%p A259236   Cands:= select(`>`,Cands union map(parse,newSubstrings), m);
%p A259236   nS:= length(S);
%p A259236 od:
%p A259236 seq(A[i],i=1..n-1); # _Robert Israel_, Jun 22 2015
%o A259236 (PARI) { dmx=1000; d=vector(dmx); b=10; for(i=1,b-1,d[i]=i;print1(i,", ")); di=b-1; n=di; while(di<dmx, n++; dig=digits(n,b); dii=1; ok=0; for(i=1,di-#dig+1, while(dii<#dig && d[i+dii-1]==dig[dii], dii++); if(dii==#dig && d[i+dii-1]==dig[dii], ok=1; i=di-#dig+1, dii=1); ); if(ok, print1(n,", "); for(i=1,#dig, di++; if(di<=dmx, d[di]=dig[i]) ); ); ); }
%Y A259236 Cf. A048991.
%K A259236 nonn,base,easy
%O A259236 1,2
%A A259236 _Anthony Sand_, Jun 22 2015