A362076 - OEIS

%I #18 Apr 09 2023 10:54:46

%S 1,2,3,4,5,6,7,8,9,10,11,22,13,14,30,15,12,23,18,20,17,16,19,21,24,26,

%T 31,25,28,29,33,32,27,35,36,34,37,39,50,38,42,40,43,44,45,46,41,47,48,

%U 49,60,51,52,70,55,61,62,54,56,57,58,59,65,64,53,66,67,63,68,69,71,72,73,74,76,77

%N a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) * a(n-1).

%C The sequence is finite; after 6481 terms a(6480) = 5211 and a(6481) = 44444 resulting in a product of 5211 * 44444 = 231597684. This contains all digits 1 to 9 so the next term does not exist.

%C The sequence contains 40 fixed points, the last being a(5477).

%H Michael S. Branicky, <a href="/A362076/b362076.txt">Table of n, a(n) for n = 1..6481</a>

%H Michael S. Branicky, <a href="/A362076/a362076_1.py.txt">Python program</a>

%H Scott R. Shannon, <a href="/A362076/a362076.png">Image of the 6481 terms</a>. The green line is a(n) = n.

%e a(12) = 22 as a(10) * a(11) = 10 * 11 = 110, and 22 is the smallest unused number that does not contain the digits 0 or 1.

%o (Python) # see linked program

%Y Cf. A362075, A342441, A342442, A067581, A297065.

%K nonn,base,fini,full

%O 1,2

%A _Scott R. Shannon_, Apr 08 2023