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, 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

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

Cf. A254596.

Sequence in context: A378293 A320109 A278062 * A064698 A373593 A320117

Adjacent sequences: A254594 A254595 A254596 * A254598 A254599 A254600

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2015

Status

approved