%I #8 Mar 28 2015 22:19:47

%S 2,4,6,8,10,11,20,23,24,28,29,32,33,34,35,41,42,45,46,47,54,56,58,60,

%T 65,67,68,70,75,77,78,81,85,89,92,94,95,99,100,101,106,107,108,109,

%U 111,124,125,128,129,130,132,133,135,140,141,143,145,146,147,152,154,156,158

%N Numbers n for which there is a unique k such that n = k + (product of nonzero digits of k).

%H %H P. A. Loomis, <a href="http://facstaff.bloomu.edu/ploomis/sequences.html">An Interesting Family of Iterated Sequences</a>

%H %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 %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 %H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%e 21 is the unique k such that k + (product of nonzero digits of k) = 23, hence 23 is a term.

%t f[n_] := Block[{s = Sort[ IntegerDigits[n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {200}]; Do[ a = f[n]; If[a < 200, t[[a]]++ ], {n, 200}]; Select[ Range[ 200], t[[ # ]] == 1 &] (* _Robert G. Wilson v_, Jul 16 2004 *)

%o (PARI) addpnd(n)=local(k,s,d);k=n;s=1;while(k>0,d=divrem(k,10);k=d[1];s=s*max(1,d[2]));n+s

%o {c=1;z=160;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))}

%Y Cf. A063114, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.

%K nonn,base

%O 1,1

%A _Klaus Brockhaus_, Jul 15 2004