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 A096922 Numbers n for which there is a unique k such that n = k + (product of nonzero digits of k). 15
 2, 4, 6, 8, 10, 11, 20, 23, 24, 28, 29, 32, 33, 34, 35, 41, 42, 45, 46, 47, 54, 56, 58, 60, 65, 67, 68, 70, 75, 77, 78, 81, 85, 89, 92, 94, 95, 99, 100, 101, 106, 107, 108, 109, 111, 124, 125, 128, 129, 130, 132, 133, 135, 140, 141, 143, 145, 146, 147, 152, 154, 156, 158 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS %H P. A. Loomis, An Interesting Family of Iterated Sequences %H P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. %H P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy] EXAMPLE 21 is the unique k such that k + (product of nonzero digits of k) = 23, hence 23 is a term. MATHEMATICA 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 *) PROG (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 {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, ", ")))} CROSSREFS Cf. A063114, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931. Sequence in context: A214671 A291171 A185449 * A241071 A319807 A055954 Adjacent sequences:  A096919 A096920 A096921 * A096923 A096924 A096925 KEYWORD nonn,base AUTHOR Klaus Brockhaus, Jul 15 2004 STATUS approved

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Last modified July 20 05:43 EDT 2019. Contains 325168 sequences. (Running on oeis4.)