A309965 a(n) is the greatest product of the digits of n in any base b in the range 2..n.

0, 1, 1, 2, 2, 3, 4, 4, 4, 6, 5, 6, 8, 9, 8, 10, 9, 12, 12, 10, 12, 15, 16, 14, 16, 18, 16, 20, 18, 21, 20, 20, 24, 25, 20, 22, 24, 28, 25, 30, 27, 30, 32, 27, 30, 35, 36, 36, 33, 36, 35, 40, 40, 42, 36, 36, 40, 45, 36, 42, 48, 49, 48, 50, 45, 48, 48, 54, 50

Offset

2,4

Links

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

Rémy Sigrist, Scatterplot of (n, n-a(n)) for n = 2..50000

Formula

a(n) < n.

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
- hence a(8) = 4.

Prog

(PARI) a(n) = vecmax(vector(n-1, b, vecprod(digits(n, b+1))))

Crossrefs

See A309969 for the corresponding base b.

Cf. A007954.

Sequence in context: A262976 A349608 A224709 * A366385 A070172 A273353

Adjacent sequences: A309962 A309963 A309964 * A309966 A309967 A309968

Keyword

nonn,base

Author

Rémy Sigrist, Aug 25 2019

Status

approved