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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.

%I A243219 #15 Nov 23 2019 04:02:57
%S A243219 5,59,599,6799,68899,689999,6999999,77899999,779999999,7889999999,
%T A243219 78999999999,799999999999,8689999999999,86999999999999,
%U A243219 878999999999999,8799999999999999,88899999999999999,889999999999999999,8989999999999999999,89999999999999999999
%N 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.
%C A243219 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.
%C A243219 a(n) <= 9*R_n for all n. Further, floor(a(n+1)/10) >= a(n) for all n. - _Derek Orr_, Jun 02 2014
%e A243219 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.
%o A243219 (PARI) DP(n)= my(d = digits(n)); prod(i=1, #d, d[i]);
%o A243219 a(n) = {for (i=10^(n-1), 10^n-1, if (i + DP(i) >= 10^n, return(i)););}
%Y A243219 Cf. A007954, A242945, A243218.
%K A243219 nonn,base
%O A243219 1,1
%A A243219 _Michel Marcus_, Jun 01 2014
%E A243219 a(10)-a(20) from _Derek Orr_, Jun 02 2014