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A254597
Convert number n to the bases from 2 to 10. For any n, sequence lists the minimum base with the highest product of digits.
2
2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 4, 7, 5, 5, 4, 6, 6, 5, 5, 7, 8, 6, 6, 5, 9, 9, 7, 6, 6, 8, 8, 7, 7, 7, 6, 10, 10, 8, 8, 7, 7, 9, 9, 9, 8, 8, 8, 7, 10, 9, 9, 9, 9, 8, 8, 10, 10, 10, 10, 9, 9, 9, 8, 10, 10, 10, 10, 10, 10, 9, 9, 5, 5, 5, 10, 10, 10, 10, 10, 9, 7
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
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
Cf. A254596.
Sequence in context: A079050 A320109 A278062 * A064698 A373593 A320117
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 02 2015
STATUS
approved