A048175 Size of range 1..m generatable from the digits of an n-digit integer and + - x /.

3, 10, 51, 192, 963, 4021

Offset

2,1

Comments

Let k be an n-digit positive integer, compute all integers that can be formed by combining the digits of k using + - x / and parentheses (but no digit concatenation, exponentiation, or other operators). Let r(k) be the largest range 1..m present in the output set. Then a(n) is the max of r(k) over all n-digit numbers.

Links

Table of n, a(n) for n=2..7.

Michael S. Branicky, Python program

Sean A. Irvine, Java program (github)

Example

a(3)=10 because 1..10 can be made from the digits of 124 ( 1=4-2-1, 2=4-(2/1), 3=4-2+1, 4=4/(2-1), 5=4+2-1, 6=4+(2/1), 7=4+2+1, 8=4*2/1, 9=4*2+1, 10=(4+1)*2 ) and no 3-digit number gives a larger range.
a(5)=192 achieved by 45678 (and its permutations), a(6)=963 achieved by 256789. - Sean A. Irvine, Jun 03 2021
a(7) achieved by 4567899. - Michael S. Branicky, Jun 28 2021

Prog

(Python) # see linked program

Crossrefs

Sequence in context: A352414 A341648 A307099 * A288953 A192482 A233537

Adjacent sequences: A048172 A048173 A048174 * A048176 A048177 A048178

Keyword

nonn,base,hard,more

Author

Mike Keith

Extensions

a(7) from Michael S. Branicky, Jun 28 2021

Status

approved