A309969 a(n) is the least base b in the range 2..n where the product of the digits of n is maximized.

2, 2, 3, 3, 4, 4, 3, 5, 4, 4, 7, 5, 5, 4, 6, 6, 5, 5, 7, 8, 6, 6, 5, 9, 9, 7, 6, 6, 8, 8, 11, 7, 7, 6, 13, 13, 8, 8, 7, 7, 11, 11, 9, 12, 8, 8, 7, 10, 13, 13, 9, 9, 11, 8, 19, 12, 10, 10, 9, 9, 9, 8, 13, 11, 17, 17, 10, 10, 12, 9, 15, 15, 15, 11, 11, 13, 10

Offset

2,1

Links

Rémy Sigrist, Table of n, a(n) for n = 2..10000

Example

For n = 8:
- the digits of 8 in bases b = 2..8 and the corresponding products are:
  b  digits  product
  -  ------  -------
  2  "1000"        0
  3    "22"        4
  4    "20"        0
  5    "13"        3
  6    "12"        2
  7    "11"        1
  8    "10"        0
- the product is maximized in base b = 3,
- hence a(8) = 3.

Prog

(PARI) a(n) = my (v, m=-1); for (b=2, n, my (p=vecprod(digits(n, b))); if (m<p, m=p; v=b)); v

Crossrefs

See A309965 for the corresponding product of digits.

Sequence in context: A339082 A329907 A329958 * A036041 A252759 A085654

Adjacent sequences: A309966 A309967 A309968 * A309970 A309971 A309972

Keyword

nonn,look,base

Author

Rémy Sigrist, Aug 25 2019

Status

approved