A336740 - OEIS

%I #10 Sep 05 2020 20:18:06

%S 110,19,10,9,1,8,101,7,3,89,12,6,18,4,2,99,13,11,27,36,49,29,102,5,21,

%T 15,22,45,111,54,28,211,14,311,38,23,411,511,31,32,47,69,104,611,17,

%U 711,56,59,103,65,112,26,811,121,113,74,41,83,212,58,911,122,16,24,63,37,131,33,92,98,25,129,105,42

%N Lexicographically earliest sequence of distinct positive terms starting with a(1) = 110 such that the successive sums of the last two digits of the sequence reproduce, digit by digit, the sequence itself.

%H Jean-Marc Falcoz, <a href="/A336740/b336740.txt">Table of n, a(n) for n = 1..10002</a>

%e After a(1) = 110 (the sum of the last two digits is 1) the smallest unused term allowing us to reconstruct the sequence by adding its last two digits is a(2) = 19 (1+9 = 10); the succession of the two sums so far is 1, 10;

%e a(3) = 10, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (1+0 = 1); the succession of the three sums so far is 1, 10, 1;

%e a(4) = 9, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (0+9 = 9); the succession of the four sums so far is 1, 10, 1, 9;

%e a(5) = 1, the smallest unused term allowing us to rebuild the sequence by adding its last two digits (9+1 = 10); the succession of the five sums so far is 1, 10, 1, 9, 10 which is precisely the succession of the sequence's digits itself. Etc.

%Y Cf. A336523 (product instead of sum).

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 02 2020