A321136 Reduced numbers with multiplicative persistence 12 in base 14.

82092087348200531993, 112762935748501480133, 262718674122383875983, 263029749260219193811, 300390025745554034372, 1121144219125164400220, 1970210218466750664277, 3677727222739184127743, 3743399183079496964351, 4597158601038676586591, 16090049120558582236269

Offset: 1

Author

A.H.M. Smeets, Oct 28 2018

Keywords

• nonn
• base

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 conjectured 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 12, it will be larger than 14^100.

a(1) = A321135(12).

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..76

Crossrefs

Cf. A321135, A321137, A321138.