A369303 - OEIS

%I #11 Jan 19 2024 08:14:08

%S 1,2,12,21,22,112,121,210,120,10,11,13,110,31,3,113,131,231,122,111,

%T 211,123,114,310,43,4,34,143,41,134,115,141,51,15,116,151,61,16,117,

%U 161,71,17,118,171,81,18,119,181,91,19,311,93,190,312,23,220,32,30,223,20,132,14,212,42,24,221

%N a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused number whose string value contains the comma transform (cf. A367360) of the previous two terms.

%C The sequence is conjectured to be a permutation of the positive integers. The fixed points begin 1, 2, 10, 11, 2863, 3164, 3545, 3947, 6835, 6947, 7052, ... although it is likely there are infinitely more.

%H Scott R. Shannon, <a href="/A369303/b369303.txt">Table of n, a(n) for n = 1..10000</a>

%H Scott R. Shannon, <a href="/A369303/a369303.png">Image of the first one million terms</a>. The green line is a(n) = n.

%e a(3) = 12 as the comma transform of 1 and 2 is 12.

%e a(6) = 112 as the comma transform of 21 and 22 is 12, but 12 has already appeared so the next lowest unused number to contain '12' is 112.

%Y Cf. A367360, A121805, A367362.

%K nonn,base,look

%O 1,2

%A _Scott R. Shannon_, Jan 19 2024