

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, 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
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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



