%I #12 Dec 15 2017 17:36:44
%S 1,2,12,102,116,1098,2072,1014,101134,11014,1011098,1003525,41021255,
%T 210110985,403130555,481104655,4401225555,4811125555,86413249555,
%U 39011218055
%N Least number with n preimages (or immediate predecessors) under f(n) = n + (product of nonzero digits of n).
%C First occurrence of k in A096972.
%C a(20) > 10^11. [From _Donovan Johnson_, Nov 22 2009]
%D P. A. Loomis, An Introduction to Digit Product Sequences (see link).
%H P. A. Loomis, <a href="http://facstaff.bloomu.edu/ploomis/sequences.html">An Interesting Family of Iterated Sequences</a>.
%H P. A. Loomis, <a href="http://facstaff.bloomu.edu/ploomis/itseq4.ps">An Introduction to Digit Product Sequences</a>, J. Rec. Math., 32 (2003-2004), 147-151.
%H P. A. Loomis, <a href="/A063108/a063108.pdf">An Introduction to Digit Product Sequences</a>, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e a(3)=102 because 102 is the least number with three direct predecessors, 66: 66+6*6 = 102, 74: 74+7*4 = 102, 101: 101+1*1 = 102.
%Y Cf. A096972, A063108, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.
%K base,more,nonn
%O 0,2
%A _Jason Earls_, Jun 29 2004
%E a(8) to a(11) from _Klaus Brockhaus_, Jul 07 2004
%E a(12) from _Robert G. Wilson v_, Jul 15 2004
%E a(13)-a(19) from _Donovan Johnson_, Nov 22 2009