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

1,1

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

Links

Table of n, a(n) for n=1..20.

Example

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.

Prog

(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)); ); }

Crossrefs

Cf. A007954, A242945, A243218.

Sequence in context: A178003 A036947 A099151 * A113055 A020468 A093946

Adjacent sequences: A243216 A243217 A243218 * A243220 A243221 A243222

Keyword

nonn,base

Author

Michel Marcus, Jun 01 2014

Extensions

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

Status

approved