A391696 Irregular triangular array read by rows: T(n,k) = position of 1st letter of 1st appearance of the k-th word of length n in the lexicographic ordering of all 01-words, as in A076478.

1, 2, 3, 5, 7, 9, 11, 14, 17, 20, 23, 26, 29, 32, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 104, 109, 114, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Example

First 4 rows:
   1    2
   3    5    7    9
  11   14   17   20   23   26   29   32
  35   39   43   47   51   55   59   63   60   71   75   79   83   87   91   95
The sequence of all 01-words in lexicographic order is (0, 1, 00, 01, 10, 11, 000, 001, 010, ...).
When these are concatenated, the result is the binary Champernowne word, A076478 = (0100011011000001010...).
a(8) = 14 because the 8th word, 001, first appears in the 14th position in A076478.

Mathematica

c[n_] := (n - 1) 2^(n + 1) + 3 (* A088578 *)
t[n_, k_] := c[n - 1] + k*n;
u = Table[t[n, k], {n, 1, 8}, {k, 0, 2^n - 1}]
Column[u]  (* A391696 array *)
Flatten[u] (* A391696 sequence *)

Crossrefs

Cf. A076478, A088578.

Sequence in context: A102422 A062427 A127721 * A292620 A241907 A065130

Adjacent sequences: A391693 A391694 A391695 * A391697 A391698 A391699

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 17 2025

Status

approved