A391696 - OEIS

%I #15 Dec 23 2025 00:11:22

%S 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,

%T 79,83,87,91,95,99,104,109,114,119,124,129,134,139,144,149,154,159,

%U 164,169,174,179,184,189,194,199,204,209,214,219,224,229,234,239

%N 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.

%e First 4 rows:

%e    1    2

%e    3    5    7    9

%e   11   14   17   20   23   26   29   32

%e   35   39   43   47   51   55   59   63   60   71   75   79   83   87   91   95

%e The sequence of all 01-words in lexicographic order is (0, 1, 00, 01, 10, 11, 000, 001, 010, ...).

%e When these are concatenated, the result is the binary Champernowne word, A076478 = (0100011011000001010...).

%e a(8) = 14 because the 8th word, 001, first appears in the 14th position in A076478.

%t c[n_] := (n - 1) 2^(n + 1) + 3 (* A088578 *)

%t t[n_, k_] := c[n - 1] + k*n;

%t u = Table[t[n, k], {n, 1, 8}, {k, 0, 2^n - 1}]

%t Column[u]  (* A391696 array *)

%t Flatten[u] (* A391696 sequence *)

%Y Cf. A076478, A088578.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Dec 17 2025