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

5, 91, 919, 7795, 100000, 1000000, 10000000, 100000000, 1000000000, 9968647168, 100000000000, 1000000000000, 9999761914432, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 9999982446427242496

Offset: 1

Author

Derek Orr, Jun 01 2014

Keywords

• nonn
• base
• hard

Comments

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

Examples

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

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A007954, A242945.

Programs

PARI

DP(n)={p=1;d=digits(n);return(prod(i=1,#d,d[i]))}
a(n)=for(k=10^n-9^n,10^n,if((k+DP(k))==10^n,return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

Extensions

a(8)-a(19) from Hiroaki Yamanouchi, Jul 10 2014