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A211027 Triangle of binary numbers >= 1 with no initial repeats. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Alois P. Heinz, Rows n = 1..15, flattened

Index entries for sequences related to curling numbers

EXAMPLE

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;

MAPLE

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:

seq(T(n), n=1..7);  # Alois P. Heinz, Dec 02 2012

MATHEMATICA

T[n_] := If[n == 1, {1}, FromDigits /@ Select[Range[2^(n-1), 2^n-2] // IntegerDigits[#, 2]&, FindTransientRepeat[Reverse[#], 2][[2]] == {}&]];

Array[T, 7] // Flatten (* Jean-François Alcover, Feb 27 2021 *)

CROSSREFS

Column 1 is A011557. Row n has length A093371(n).

Cf. A122536, A211029, A211968, A211969, A216955.

Sequence in context: A037415 A123001 A014417 * A328072 A185101 A007924

Adjacent sequences:  A211024 A211025 A211026 * A211028 A211029 A211030

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Nov 30 2012

STATUS

approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)