cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Michel Marcus, Jun 01 2014

Keywords

Examples

			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.
		

Crossrefs

Programs

  • PARI
    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;}

Extensions

a(9)-a(17) from Hiroaki Yamanouchi, Sep 29 2014
a(18)-a(20) from Hiroaki Yamanouchi, Jan 08 2016

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

Views

Author

Derek Orr, Jun 01 2014

Keywords

Comments

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

Examples

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

Crossrefs

Programs

  • 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++)

Extensions

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

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

Views

Author

Michel Marcus, Jun 01 2014

Keywords

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

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
Showing 1-3 of 3 results.