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%I #6 Jun 23 2019 09:55:06
%S 1,2,3,4,7,6,5,8,9,11,10,13,12,17,14,15,16,19,18,20,21,22,25,24,23,26,
%T 27,28,30,31,34,33,29,35,32,39,38,42,41,44,36,37,43,40,45,46,49,51,47,
%U 48,50,53,54,55,52,57,56,60,58,64,61,66,65,62,63,59,69,68,72,71,74,75,70,73,67,79,76,82,81,77,78,80,83
%N Lexicographically earliest sequence of distinct terms such that the digits of two contiguous terms sum up to a prime.
%C It is conjectured that this sequence is a permutation of the integers > 0.
%H Jean-Marc Falcoz, <a href="/A308728/b308728.txt">Table of n, a(n) for n = 1..10001</a>
%e The sequence starts with 1,2,3,4,7,6,5,8,9,11,10,13,... and we see indeed that the digits of:
%e {a(1); a(2)} have sum 1 + 2 = 3 (prime);
%e {a(2); a(3)} have sum 2 + 3 = 5 (prime);
%e {a(3); a(4)} have sum 3 + 4 = 7 (prime);
%e {a(4); a(5)} have sum 4 + 7 = 11 (prime);
%e {a(5); a(6)} have sum 7 + 6 = 13 (prime);
%e {a(6); a(7)} have sum 6 + 5 = 11 (prime);
%e {a(7); a(8)} have sum 5 + 8 = 13 (prime);
%e {a(8); a(9)} have sum 8 + 9 = 17 (prime);
%e {a(9); a(10)} have sum 9 + 1 + 1 = 11 (prime);
%e {a(10); a(11)} have sum 1 + 1 + 1 + 0 = 3 (prime);
%e {a(11); a(12)} have sum 1 + 0 + 1 + 3 = 5 (prime);
%e etc.
%Y Cf. A308719 (same idea with palindromes) and A308727 (with squares).
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 20 2019
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