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A321149 a(1) = 102735, a(n) = prime(n-1)*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.

%I A321149 #13 Nov 04 2018 00:11:29
%S A321149 102735,2547,7641,38205,267435,2941785,8405,1425,205,4715,1675,192,
%T A321149 7104,9164,394052,18520,981560,579124,24,1608,468,316,296,24568,186,
%U A321149 18042,184,18952,7864,8516,962308,36
%N A321149 a(1) = 102735, a(n) = prime(n-1)*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.
%C A321149 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 A321149 102735 is the smallest of 785 A010784 terms that result in a 362-term sequence, the longest possible.
%H A321149 Hans Havermann, <a href="/A321149/b321149.txt">Table of n, a(n) for n = 1..362</a>
%H A321149 Hans Havermann, <a href="http://gladhoboexpress.blogspot.com/2018/10/whats-so-special-about-102735.html">What's so special about 102735?</a>
%e A321149 2 * 102735 = [205470] => 2547
%e A321149 3 * 2547 = 7641
%e A321149 5 * 7641 = 38205
%e A321149 7 * 38205 = 267435
%e A321149 11 * 267435 = 2941785
%e A321149 13 * 2941785 = [38243205] => 8405
%e A321149 17 * 8405 = [142885] => 1425
%e A321149 19 * 1425 = [27075] => 205
%e A321149 ...
%e A321149 2417 * 40 = [96680] => 980
%e A321149 2423 * 980 = [2374540] => 23750
%e A321149 2437 * 23750 = [57878750] => 0
%Y A321149 Cf. A010784, A321148, A320486.
%K A321149 nonn,fini,full,base
%O A321149 1,1
%A A321149 _Hans Havermann_, Oct 28 2018