OFFSET
1,1
COMMENTS
For n <= 10^6 the frequencies are:
2 -> 1 (highest number: 1)
3 -> 1 (highest number: 2)
4 -> 19 (highest number: 48890)
5 -> 26217 (highest number: 999909)
6 -> 66790 (highest number: 1000000)
7 -> 123289 (highest number: 999990)
8 -> 187650 (highest number: 999423)
9 -> 236499 (highest number: 999980)
10 -> 359534 (highest number: 999999)
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..1000
EXAMPLE
1 in base 2 is 1011 -> product of digits: 0;
11 in base 3 is 102 -> product of digits: 0;
11 in base 4 is 23 -> product of digits: 6;
11 in base 5 is 21 -> product of digits: 2;
11 in base 6 is 15 -> product of digits: 5;
11 in base 7 is 14 -> product of digits: 4;
11 in base 8 is 13 -> product of digits: 3;
11 in base 9 is 12 -> product of digits: 2;
11 in base 10 is 11 -> product of digits: 1.
Therefore a(11) = 4.
MAPLE
with(numtheory): P:=proc(q) local a, b, c, d, j, k, n;
for n from 1 to q do c:=0;
for k from 2 to 10 do a:=convert(n, base, k);
b:=mul(a[j], j=1..nops(a)); if b>c then c:=b; d:=k;
fi; od; print(d); od; end: P(10^4);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 02 2015
STATUS
approved