cp's OEIS Frontend

A308232 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the concatenation kd, d being the digit that was read and k the number of d's present so far in the sequence.

%I A308232 #19 May 25 2019 12:12:49
%S A308232 1,11,21,31,12,41,13,51,61,22,14,71,81,23,15,91,16,101,32,42,111,24,
%T A308232 17,121,18,131,52,33,141,25,19,151,161,26,171,10,181,43,62,34,72,191,
%U A308232 201,211,82,44,221,27,231,92,241,251,28,261,53,271,35,102,63,73,281,54,291,112,45,301,29,311,55,321,331,36,341,122,46,351
%N A308232 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the concatenation kd, d being the digit that was read and k the number of d's present so far in the sequence.
%C A308232 All integers > 0 will appear exactly once, except 2, 3, 4, 5, 6, 7, 8 and 9 which will never appear.
%H A308232 Carole Dubois, <a href="/A308232/b308232.txt">Table of n, a(n) for n = 1..5001</a>
%H A308232 Carole Dubois, <a href="/A308232/a308232.png">Digit count for three sequences (see Xrefs)</a>
%H A308232 Carole Dubois, <a href="/A308232/a308232_1.png">Digit-count for this sequence and two others visible in the Xref section</a>
%e A308232 The sequence starts with a(1) = 1.
%e A308232 We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then [kd] = 11 and this 11 becomes a(2);
%e A308232 We read now the first digit of a(2) = 11, which is 1; as this 1 is the 2nd occurrence of 1 so far in the sequence, we have k = 2 and [kd] = 21; this 21 becomes a(3);
%e A308232 We read now the second digit of a(2) = 11, which is 1; as this 1 is the 3rd occurrence of 1 so far in the sequence, we have k = 3 and [kd] = 31; this 31 becomes a(4);
%e A308232 We read now the first digit of a(3) = 21, which is 2; as this 2 is the 1st occurrence of 2 so far in the sequence, we have k = 1 and [kd] = 12; this 12 becomes a(5);
%e A308232 We read now the second digit of a(3) = 21, which is 1; as this 1 is the 4th occurrence of 1 so far in the sequence, we have k = 4 and [kd] = 41; this 41 becomes a(6); etc.
%Y A308232 Cf. A325721 and A325722 where the same idea is developed (addition and multiplication instead of concatenation).
%K A308232 base,nonn
%O A308232 1,2
%A A308232 _Eric Angelini_ and _Carole Dubois_, May 16 2019