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A291072
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Take n-th string over {1,2} in lexicographic order and apply the Watanabe tag system {00, 1011} described in A291067 (but adapted to the alphabet {1,2}) just once.
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6
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-1, 22, 1, 1, 122, 122, 11, 11, 11, 11, 2122, 2122, 2122, 2122, 111, 211, 111, 211, 111, 211, 111, 211, 12122, 22122, 12122, 22122, 12122, 22122, 12122, 22122, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 1111, 1211, 2111, 2211, 112122, 122122, 212122, 222122
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OFFSET
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1,2
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LINKS
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MAPLE
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# First define the mapping by defining the strings T1 and T2:
# Work over the alphabet {1, 2}
# 11 / 2212 A284116 This is the "Post Tag System"
T1:="11"; T2:="2212";
# 11 / 2122 A291067 These three are from the Watanabe paper
T1:="11"; T2:="2122";
T1:="11"; T2:="2221";
T1:="11"; T2:="1222";
with(StringTools):
# the mapping:
f1:=proc(w) local L, ws, w2; global T1, T2;
ws:=convert(w, string);
if ws="-1" then return("-1"); fi;
if ws[1]="1" then w2:=Join([ws, T1], ""); else w2:=Join([ws, T2], ""); fi;
L:=length(w2); if L <= 3 then return("-1"); fi;
w2[4..L]; end;
# Construct list of words over {1, 2} (A007931)
a:= proc(n) local m, r, d; m, r:= n, 0;
while m>0 do d:= irem(m, 2, 'm');
if d=0 then d:=2; m:= m-1 fi;
r:= d, r
od; parse(cat(r))/10
end:
WLIST := [seq(a(n), n=1..100)];
# apply the map once:
W2:=map(f1, WLIST);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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