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%I #6 Jun 23 2019 09:54:51
%S 1,3,6,12,10,8,17,26,35,44,53,62,71,80,89,107,98,116,100,21,15,19,24,
%T 28,33,30,42,37,51,46,60,55,69,64,78,73,87,82,96,91,105,102,49,39,4,5,
%U 13,14,22,23,29,32,31,41,38,50,40,48,58,57,67,66,76,75,85,84,94,93,103,104,47,59,2,7,9,16,11,20,25,18,34,27,43,36,52
%N Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a square.
%C It is conjectured that this sequence is a permutation of the integers > 0.
%H Jean-Marc Falcoz, <a href="/A308727/b308727.txt">Table of n, a(n) for n = 1..10001</a>
%e The sequence starts with 1,3,6,12,10,8,17,26,... and we see indeed that the digits of:
%e {a(1); a(2)} have sum 1 + 3 = 4 (square);
%e {a(2); a(3)} have sum 3 + 6 = 9 (square);
%e {a(3); a(4)} have sum 6 + 1 + 2 = 9 (square);
%e {a(4); a(5)} have sum 1 + 2 + 1 + 0 = 4 (square);
%e {a(5); a(6)} have sum 8 + 1 + 7 = 16 (square);
%e {a(6); a(7)} have sum 1 + 7 + 2 + 6 = 16 (square);
%e etc.
%Y Cf. A308719 (same idea with palindromes instead of squares).
%K base,nonn
%O 1,2
%A _Jean-Marc Falcoz_ and _Eric Angelini_, Jun 20 2019
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