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A243198 Least number k such that k + DigProd(k) = 10^n. 1

%I

%S 5,91,919,7795,100000,1000000,10000000,100000000,1000000000,

%T 9968647168,100000000000,1000000000000,9999761914432,100000000000000,

%U 1000000000000000,10000000000000000,100000000000000000,1000000000000000000,9999982446427242496

%N Least number k such that k + DigProd(k) = 10^n.

%C a(n) <= 10^n for all n.

%H Hiroaki Yamanouchi, <a href="/A243198/b243198.txt">Table of n, a(n) for n = 1..50</a>

%e 919 + 9*1*9 = 1000 = 10^3. Since 919 is the smallest number with this property, a(3) = 919.

%o (PARI) DP(n)={p=1;d=digits(n);return(prod(i=1,#d,d[i]))}

%o a(n)=for(k=10^n-9^n,10^n,if((k+DP(k))==10^n,return(k)))

%o n=1;while(n<100,print1(a(n),", ");n++)

%Y Cf. A007954, A242945.

%K nonn,base,hard

%O 1,1

%A _Derek Orr_, Jun 01 2014

%E a(8)-a(19) from _Hiroaki Yamanouchi_, Jul 10 2014

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)