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A321148 a(1) = 24603, a(n) = n*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.

%I A321148 #15 Nov 04 2018 00:12:35
%S A321148 24603,49206,4768,19072,95360,572160,4512,309,2781,27810,3591,43092,
%T A321148 5019,702,153,28,476,56,1064,180,3780,83160,92680,430,175,40,18,504,4,
%U A321148 120,3720,94,3102,105468,69180,298,26,9,351,1,41,17,731,32164,17380,7480,3160,5680,7830,3915,15,780,130,72,3960,1760,132,75,25,15,915,56730,570,36480,371,286,962,541,729,513,642,6,438,341,27,5,385,0
%N A321148 a(1) = 24603, a(n) = n*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.
%C A321148 At each step, integers that contain duplicated digits are reduced to terms of A010784 by erasing all digits that appear more than once and bunching up the digits that remain. Leading zeros are ignored and any number that disappears entirely becomes 0. See A320486.
%C A321148 24603 is the smallest of 1746 A010784 terms that result in a 78-term sequence, the longest possible.
%H A321148 Hans Havermann, <a href="http://gladhoboexpress.blogspot.com/2018/10/whats-so-special-about-102735.html">What's so special about 102735?</a>
%e A321148 2 * 24603 = 49206
%e A321148 3 * 49206 = [147618] => 4768
%e A321148 4 * 4768 = 19072
%e A321148 5 * 19072 = 95360
%e A321148 6 * 95360 = 572160
%e A321148 7 * 572160 = [4005120] => 4512
%e A321148 8 * 4512 = [36096] => 309
%e A321148 ...
%e A321148 76 * 27 = [2052] => 5
%e A321148 77 * 5 = 385
%e A321148 78 * 385 = [30030] => 0
%Y A321148 Cf. A010784, A321149, A320486.
%K A321148 nonn,fini,full,base
%O A321148 1,1
%A A321148 _Hans Havermann_, Oct 28 2018