A333722 - OEIS

%I #20 Apr 13 2020 11:44:28

%S 1,10,11,12,2,21,15,5,25,29,28,24,22,26,6,16,36,37,39,34,14,13,3,31,

%T 23,27,71,7,97,69,56,45,35,38,18,48,8,81,17,47,42,44,41,4,46,40,20,30,

%U 50,51,52,53,55,57,65,54,49,19,61,60,66,76,64,62,63,96,67,68,85,59,75,58,83,33,93,43,32,72,92,98,80,70,90,91,9

%N Lexicographically earliest permutation of the positive integers such that a(n), a(n+1) and the product a(n)*a(n+1) have in common at least one identical substring.

%H Jean-Marc Falcoz, <a href="/A333722/b333722.txt">Table of n, a(n) for n = 1..20002</a>

%e a(1) = 1 and a(2) = 10 share with their product 10 the substring 1;

%e a(2) = 10 and a(3) = 11 share with their product 110 the substring 1;

%e a(3) = 11 and a(4) = 12 share with their product 132 the substring 1;

%e a(4) = 12 and a(5) = 2 share with their product 24 the substring 2;

%e a(5) = 2 and a(6) = 21 share with their product 42 the substring 2; etc.

%Y Cf. A333723 (lists the products a(n) * a(n+1) in their order of appearance here), A333724 (lists the biggest substring shared by a(n), a(n+1) and (a(n)*a(n+1)) in their order of appearance here), A262323 (is the lexicographically earliest sequence of distinct terms such that the decimal representations of two consecutive terms overlap).

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 03 2020