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

1,1

Comments

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

Links

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

Example

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

Prog

(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++)

Crossrefs

Cf. A007954, A242945.

Sequence in context: A152299 A355371 A242945 * A091281 A343009 A368776

Adjacent sequences: A243195 A243196 A243197 * A243199 A243200 A243201

Keyword

nonn,base,hard

Author

Derek Orr, Jun 01 2014

Extensions

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

Status

approved