A243219 Smallest n-digit integer x such that x + A007954(x) has n+1 digits, where A007954(x) is the product of decimal digits of x.

5, 59, 599, 6799, 68899, 689999, 6999999, 77899999, 779999999, 7889999999, 78999999999, 799999999999, 8689999999999, 86999999999999, 878999999999999, 8799999999999999, 88899999999999999, 889999999999999999, 8989999999999999999, 89999999999999999999

Offset: 1

Author

Michel Marcus, Jun 01 2014

Keywords

• nonn
• base

Comments

The related sequence with x the largest n-digit number such that x + A007954(x) also has n digits would be 4, 90, 990, 9990, 99990, ..., etc.

a(n) <= 9*R_n for all n. Further, floor(a(n+1)/10) >= a(n) for all n. - Derek Orr, Jun 02 2014

Examples

			5 is the smallest integer with 1 digit such that 5 + A007954(5) has 2 digits, with result 5 + 5 = 10, hence a(1)=5.
		

Crossrefs

Cf. A007954, A242945, A243218.

Programs

PARI

DP(n)= my(d = digits(n)); prod(i=1, #d, d[i]);
a(n) = {for (i=10^(n-1), 10^n-1, if (i + DP(i) >= 10^n, return(i)););}

Extensions

a(10)-a(20) from Derek Orr, Jun 02 2014