%I #17 Jul 06 2024 11:54:31
%S 3,10,51,192,963,4021
%N Size of range 1..m generatable from the digits of an n-digit integer and + - x /.
%C 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.
%H Michael S. Branicky, <a href="/A048175/a048175.txt">Python program</a>
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048175.java">Java program</a> (github)
%e 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.
%e a(5)=192 achieved by 45678 (and its permutations), a(6)=963 achieved by 256789. - _Sean A. Irvine_, Jun 03 2021
%e a(7) achieved by 4567899. - _Michael S. Branicky_, Jun 28 2021
%o (Python) # see linked program
%K nonn,base,hard,more
%O 2,1
%A _Mike Keith_
%E a(7) from _Michael S. Branicky_, Jun 28 2021