login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A320723
Reduced numbers with multiplicative persistence 9 in base 15.
3
30104309, 100129033, 109845884, 451564392, 622423768, 916946759, 6799389524, 9336252149, 19587821624, 98891779017, 255373745624, 1499291015624, 1532242466549, 2023768276633, 2636118566533, 2644378346249, 4324878052633, 5560581801133, 22242792374999
OFFSET
1,1
COMMENTS
Let p_15(n) be the product of the digits of n in base 15. We can define an equivalence relation DP_15 on n by n DP_15 m if and only if p_15(n) = p_15(m); the naming DP_b for the equivalence relation stands for "digits product for representation in base b". A number n is called the class representative number of class n/DP_15 if and only if p_15(n) = p_15(m), m >= n; i.e., the smallest number of that class; it is also called the reduced number.
For any multiplicative persistence, except the multiplicative persistence 2, the set of class representative numbers with that multiplicative persistence is conjectured to be finite. Each class representative number represents an infinite set of numbers with the same multiplicative persistence.
If there exists a next reduced number m with multiplicative persistence 9, p(m) will be larger than 15^100, where p(m) is the product of the digits of m.
a(1) = A320721(9).
LINKS
EXAMPLE
The number 30104309 represented in base 15, with A..E for 10..14 is 2999BDE. Other numbers with the same reduced number are for instance: 23399BDE,2999BD27, 12999BDE; or any number obtained by permutation of the digits of those numbers.
CROSSREFS
Sequence in context: A168515 A287384 A107619 * A187431 A204346 A263644
KEYWORD
nonn,base
AUTHOR
A.H.M. Smeets, Oct 19 2018
STATUS
approved