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A336523 Lexicographically earliest sequence of distinct positive terms starting with a(1) = 0 and a(2) = 1 such that the product of the last two digits of the sequence rebuilds, digit after digit, the sequence itself.

%I A336523 #16 Jan 07 2022 19:35:59
%S A336523 0,1,11,111,211,311,411,26,511,611,3,711,27,811,34,16,15,911,28,1011,
%T A336523 1111,13,17,1211,43,71,8,1311,1411,31,4,44,35,19,1511,62,18,25,1611,
%U A336523 1711,1811,1911,2011,2111,2211,113,2311,7,126,2411,72,131,117,29,2511,213,2611,2711,127,2811,2911,231,172,2
%N A336523 Lexicographically earliest sequence of distinct positive terms starting with a(1) = 0 and a(2) = 1 such that the product of the last two digits of the sequence rebuilds, digit after digit, the sequence itself.
%H A336523 Jean-Marc Falcoz, <a href="/A336523/b336523.txt">Table of n, a(n) for n = 1..10002</a>
%e A336523 After a(1) = 0 and a(2) = 1, the smallest unused term a(3) allowing the rebuilding of the sequence by multiplying its last two digits is 11 (1*1 = 1); now the succession of such products is 0, 1;
%e A336523 after a(3) = 11, the smallest unused term a(4) allowing the rebuilding of the sequence by multiplying its last two digits is 111 (as the product of the last two digits of 111 is 1*1 = 1); now the succession of the products is 0, 1, 1);
%e A336523 after a(4) = 111, the smallest unused term a(5) allowing the rebuilding of the sequence by multiplying its last two digits is 211 (as the product of the last two digits of 211 is 1*1 = 1); now the succession of the products is 0, 1, 1, 1);
%e A336523 after a(5) = 211, the smallest unused term a(6) allowing the rebuilding of the sequence by multiplying its last two digits is 311 (as the product of the last two digits of 311 is 1*1 = 1); now the succession of the products is 0, 1, 1, 1, 1);
%e A336523 after a(6) = 311 and a(7) = 411 the smallest unused term a(8) allowing the rebuilding of the sequence by multiplying its last two digits is 26 (as the product of the last two digits of 26 is 2*6 = 12); now the succession of the products is 0, 1, 1, 1, 1, 1, 1, 2 which is the succession of the sequence's digits itself); etc.
%Y A336523 Cf. A335214.
%K A336523 base,nonn
%O A336523 1,3
%A A336523 _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 24 2020