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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

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: 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.)