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Lexicographically first sequence of distinct nonnegative terms whose succession of digits is the same as in its associated sequence T (see the Comments section for T).
2

%I #12 Sep 23 2018 22:47:36

%S 21,10,1,910,11,8,2,91,71,12,78,9,210,22,5,3,61,13,710,211,14,101,23,

%T 32,92,15,24,610,25,6,81,93,911,212,110,26,31,16,921,102,213,33,711,

%U 103,214,27,1010,17,221,28,18,310,29,3110,19,111,104,222,105,62,4,51,1110,106,41,121,107,611,231,215,216,52,82,131

%N Lexicographically first sequence of distinct nonnegative terms whose succession of digits is the same as in its associated sequence T (see the Comments section for T).

%C T(n) is the sum [last digit of a(n) + first digit of a(n+1)].

%H Lars Blomberg, <a href="/A318648/b318648.txt">Table of n, a(n) for n = 1..3999</a>

%e The sequence starts with 21, 10, 1, 910, 11, 8, 2, 91, 71, 12, ...

%e Let's make the successive sums of [the last digit of a(n) + the first digit of a(n+1)]; we have [1+1] = 2; then [0+1] = 1; then [1+9] = 10; then [0+1] = 1; then [1+8] = 9; then [8+2] = 10; then [2+9] = 11; then [1+7] = 8; then [1+1] = 2; etc.

%e Those successive sums build the sequence T = 2, 1, 10, 1, 9, 10, 11, 8, 2, ... and T shows indeed the same succession of digits as the starting sequence.

%Y Cf. A318647 for the product (instead of the sum) of the digits "framing a comma" in the sequence.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 31 2018