A291072 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.

-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

Offset: 1

Author

N. J. A. Sloane, Aug 18 2017

Keywords

• sign

Crossrefs

Cf. A007931, A284116, A291067, A291068, A291069.

Cf. also A289673, A291073, A291074.

Programs

Maple

# 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";
# 11 / 2221 A291068
T1:="11"; T2:="2221";
# 11 / 1222 A291069
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:
# this produces A289673, A291072, A291073, A291074
W2:=map(f1,WLIST);