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A338942 Lexicographically earliest sequence of distinct positive terms such that a(n) is present in 3*a(n+1).

%I A338942 #19 Dec 22 2024 09:05:22
%S A338942 1,4,8,6,2,7,9,3,10,34,78,26,42,14,38,46,82,94,98,66,22,74,58,86,62,
%T A338942 54,18,60,20,40,80,160,534,178,594,198,660,220,734,578,526,842,614,
%U A338942 538,846,282,940,980,1660,5534,5178,1726,5754,1918,6394,8798,6266,5422,8474,6158,5386,8462,6154,8718,2906,4302,1434,478
%N A338942 Lexicographically earliest sequence of distinct positive terms such that a(n) is present in 3*a(n+1).
%C A338942 The lexicographically earliest sequence of positive terms such that a(n) is present in 2*a(n+1) is A000351 (the powers of 5).
%C A338942 Conjecture: For n >= 222, a(n) = 100*a(n-16). - _Jason Yuen_, Dec 22 2024
%H A338942 Carole Dubois, <a href="/A338942/b338942.txt">Table of n, a(n) for n = 1..270</a>
%e A338942 a(1) = 1 is present (as a substring) in 12 [= 3 * a(n+1) = 3 * 4];
%e A338942 a(2) = 4 is present in 24 (= 3 * 8);
%e A338942 a(3) = 8 is present in 18 (= 3 * 6);
%e A338942 a(4) = 6 is present in 6 (= 3 * 2); etc.
%o A338942 (Magma) a:=[1]; f:=func<n,m|IntegerToString(n) in IntegerToString(m)>; for n in [2..70] do k:=2; while k in a or not f(a[n-1],3*k) do k:=k+1; end while; Append(~a,k); end for; a; // _Marius A. Burtea_, Nov 19 2020
%Y A338942 Cf. A210013, A000351.
%K A338942 base,nonn
%O A338942 1,2
%A A338942 _Eric Angelini_ and _Carole Dubois_, Nov 17 2020