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