OFFSET

1,1

COMMENTS

Numbers that are pandigital in base 2 (i.e., numbers whose digits include at least one each of 0 and 1) are 2=10_2, 4=100_2, 5=101_2, 6=110_2, 8=1000_2, etc. (i.e., all positive integers not of the form 2^j-1); exactly 2/2=1 of the first 2 positive integers and exactly 4/2=2 of the first 4 positive integers are base-2 pandigital, so 2 and 4 are in the sequence. For all k > 4, there are more base-2 pandigital numbers in 1..k than base-2 nonpandigital numbers, so there are no more terms in the n=2 row.

In base 3, exactly half of the integers in 1..174 are pandigital, so 174 is in the sequence. Fewer than half of the integers in 1..k are pandigital for all k < 174, and more than half of the integers in 1..k are pandigital for all k > 174, so 174 is the only term in the n=3 row.

The 27-digit number 245836727707164139860503406, which is a(134), is the only term in the n=10 row: in base 10, exactly half of the integers in 1..a(134) are pandigital, fewer than half of the integers in 1..k are pandigital for all k < a(134), and more than half of the integers in 1..k are pandigital for all k > a(134).

For each of rows 2 through 10, the number of terms and a list of those terms (abridged for rows 5 and 6) are as follows:

Row # terms list of terms

==== ======= ===========================================

2 2 2, 4

3 1 174

4 1 20056

5 46 9026066, 9612284, ..., 10384656;

6 80 12436651810, 12438872740, ..., 13770404636;

7 1 45381851638748

8 1 282633399694638258

9 1 9255986333928835642154

10 1 245836727707164139860503406

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..134

CROSSREFS

KEYWORD

nonn,tabf,base

AUTHOR

Jon E. Schoenfield, Aug 04 2015, expanded Aug 07 2015

STATUS

approved