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A211027
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Triangle of binary numbers >= 1 with no initial repeats.
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6
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1, 10, 100, 101, 1000, 1001, 1011, 10000, 10001, 10010, 10011, 10110, 10111, 100000, 100001, 100010, 100011, 100101, 100110, 100111, 101100, 101110, 101111, 1000000, 1000001, 1000010, 1000011, 1000100, 1000101, 1000110, 1000111, 1001010, 1001011, 1001100, 1001101, 1001110, 1001111, 1011000, 1011001, 1011100, 1011101, 1011110, 1011111
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Triangle read by rows in which row n lists the binary numbers with n digits and with no initial repeats.
Also triangle read by rows in which row n lists the binary words of length n with no initial repeats and with initial digit 1. See also A211029.
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LINKS
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EXAMPLE
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Triangle begins:
1;
10;
100, 101;
1000, 1001, 1011;
10000, 10001, 10010, 10011, 10110, 10111;
100000, 100001, 100010, 100011, 100101, 100110, 100111, 101100, 101110, 101111;
1000000, 1000001, 1000010, 1000011, 1000100, 1000101, 1000110, 1000111, 1001010, 1001011, 1001100, 1001101, 1001110, 1001111, 1011000, 1011001, 1011100, 1011101, 1011110, 1011111;
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MAPLE
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s:= proc(n) s(n):= `if`(n=1, [[1]], map(x->
[[x[], 0], [x[], 1]][], s(n-1))) end:
T:= proc(n) map(x-> parse(cat(x[])), select(proc(l) local i;
for i to iquo(nops(l), 2) do if l[1..i]=l[i+1..2*i]
then return false fi od; true end, s(n)))[] end:
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MATHEMATICA
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T[n_] := If[n == 1, {1}, FromDigits /@ Select[Range[2^(n-1), 2^n-2] // IntegerDigits[#, 2]&, FindTransientRepeat[Reverse[#], 2][[2]] == {}&]];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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