A321138 Reduced numbers with multiplicative persistence 10 in base 14.

397912927, 5449646691, 7987762047, 8408836868, 8416865813, 14311910772, 95358760419, 95359835871, 119207613951, 119319977811, 178002991683, 181182645587, 268593608191, 780359955604, 781941158165, 802715724229, 985373000485, 986970420491, 1068017311927, 1068025296336

Offset

1,1

Comments

Let p_14(n) be the product of the digits of n in base 14. We can define an equivalence relation DP_14 on n by n DP_14 m if and only if p_14(n) = p_14(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_14 if and only if p_14(n) = p_14(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 supposed to be finite. Each class representative number represents an infinite set of numbers with the same multiplicative persistence.

If there exists more reduced numbers with multiplicative persistence 10, it will be larger than 14^100.

a(1) = A321135(10).

Links

Table of n, a(n) for n=1..20.

Example

The number 397912927 represented in base 14, with A..D for 10..13 is 3ABBDDDD. Other numbers with the same reduced number are for instance 325BBDDDD or 13ABBDDDD; or any number obtained by permutation of the digits of those numbers.

Crossrefs

Cf. A321135, A321136, A321137.

Sequence in context: A175280 A271022 A015369 * A103773 A172602 A108212

Adjacent sequences: A321135 A321136 A321137 * A321139 A321140 A321141

Keyword

nonn,base

Author

A.H.M. Smeets, Oct 28 2018

Status

approved