A321136 Reduced numbers with multiplicative persistence 12 in base 14.

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

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 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.

Sequence in context: A172577 A276972 A280298 * A135955 A104840 A290156

Adjacent sequences: A321133 A321134 A321135 * A321137 A321138 A321139

Keyword

nonn,base

Author

A.H.M. Smeets, Oct 28 2018

Status

approved