A243218
Number of n-digit integers x such that x + A007954(x) has n digits, where A007954(x) is the product of decimal digits of x.
Original entry on oeis.org
5, 63, 756, 8268, 86225, 880519, 8898517, 89471520, 897248572, 8985712192, 89925825853, 899614672173, 8997997446679, 89989593213308, 899945924502919, 8999718992342921, 89998539650321017, 899992410699128981, 8999960560129165187, 89999795045731606967
Offset: 1
For n=1, the five 1-digit integers 0,1,2,3,4 satisfy the condition, with results being respectively 0,2,4,6 and 8, hence a(1)=5.
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DP(n)= my(d = digits(n)); prod(i=1, #d, d[i]);
a(n) = {nb = 0; if (n==1, istart = 0, istart = 10^(n-1)); for (i=istart, 10^n-1, if (i + DP(i) < 10^n, nb++);); nb;}
A243198
Least number k such that k + DigProd(k) = 10^n.
Original entry on oeis.org
5, 91, 919, 7795, 100000, 1000000, 10000000, 100000000, 1000000000, 9968647168, 100000000000, 1000000000000, 9999761914432, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 9999982446427242496
Offset: 1
919 + 9*1*9 = 1000 = 10^3. Since 919 is the smallest number with this property, a(3) = 919.
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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++)
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.
Original entry on oeis.org
5, 59, 599, 6799, 68899, 689999, 6999999, 77899999, 779999999, 7889999999, 78999999999, 799999999999, 8689999999999, 86999999999999, 878999999999999, 8799999999999999, 88899999999999999, 889999999999999999, 8989999999999999999, 89999999999999999999
Offset: 1
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.
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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)););}
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