A096922 Numbers n for which there is a unique k such that n = k + (product of nonzero digits of k).

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

Offset

1,1

Links

Table of n, a(n) for n=1..63.

%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]

%H Index entries for Colombian or self numbers and related sequences

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: A291171 A334614 A185449 * A241071 A353026 A356431

Adjacent sequences: A096919 A096920 A096921 * A096923 A096924 A096925

Keyword

nonn,base

Author

Klaus Brockhaus, Jul 15 2004

Status

approved