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
Examples
21 is the unique k such that k + (product of nonzero digits of k) = 23, hence 23 is a term.
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]
- %H Index entries for Colombian or self numbers and related sequences
Crossrefs
Programs
-
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 *) -
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,",")))}