|
| |
|
|
A328288
|
|
Triangle T(m,n) = # { k | concat(mk,nk) has no digit twice or more }, m >= n >= 0.
|
|
3
|
|
|
|
0, 986409, 0, 438404, 304, 0, 572175, 153, 157, 0, 219202, 197, 124, 97, 0, 109601, 221, 156, 69, 171, 0, 255752, 73, 88, 142, 68, 69, 0, 140515, 129, 73, 81, 86, 62, 46, 0, 109601, 189, 88, 40, 67, 48, 51, 24, 0, 432645, 89, 80, 77, 31, 63, 68, 41, 20, 0, 0, 0, 132, 80, 90, 58, 32, 63, 99, 37, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
This is an extended version of A328277 which is restricted to m > n >= 1.
One may consider T(m,n) defined for all m, n >= 0, which would yield a symmetric, infinite square array T(m,n), see formula.
For m and/or n = 0, see A328287(n) = T(0,n) = T(n,0), n >= 0.
The table is finite in the sense that T(m,n) = 0 for m > 987654321 (even if the multiple isn't pandigital, (mk, nk) cannot have more than 9+1 distinct digits), but also whenever the total number of digits of m and n exceeds 10.
|
|
|
LINKS
|
Table of n, a(n) for n=0..65.
M. F. Hasler, in reply to E. Angelini, Fractions with no repeated digits, SeqFan list, Oct. 10, 2020.
|
|
|
FORMULA
|
T(m,n) = 0 whenever m == n (mod 10).
T(m,n) = T(n,m) for all m, n >= 0, if the condition m > n is dropped.
|
|
|
EXAMPLE
|
The table reads :
0, (m=0)
986409, 0, (m=1)
438404, 304, 0, (m=2)
572175, 153, 157, 0, (m=3)
219202, 197, 124, 97, 0, (m=4)
109601, 221, 156, 69, 171, 0, (m=5)
255752, 73, 88, 142, 68, 69, 0, (m=6)
140515, 129, 73, 81, 86, 62, 46, 0, (m=7)
109601, 189, 88, 40, 67, 48, 51, 24, 0, (m=8)
432645, 89, 80, 77, 31, 63, 68, 41, 20, 0, (m=9)
0, 0, 132, 80, 90, 58, 32, 63, 99, 37, 0, (m=10)
90212, 0, 106, 69, 79, 50, 30, 45, 30, 38, 0, 0, (m=11)
127163, 76, 0, 96, 31, 62, 54, 27, 31, 49, 41, 27, 0, (m=12)
75768, 84, 72, 0, 31, 58, 47, 26, 23, 34, 43, 25, 20, 0, (m=13)
62436, 100, 64, 52, 0, 51, 44, 51, 42, 22, 38, 27, 18, 20 0, (m=14)
...
The terms corresponding to T(2,1) = 304 and T(3,1) = 153 are given in Eric Angelini's post to the SeqFan list.
Column 0 is A328287 (number of multiples of m that have only distinct and nonzero digits.
|
|
|
PROG
|
(PARI) T(m, n)=if(min(m, n), A328277(m, n), A328287(max(m, n))
|
|
|
CROSSREFS
|
Sequence in context: A205656 A206185 A205367 * A328287 A083395 A106782
Adjacent sequences: A328285 A328286 A328287 * A328289 A328290 A328291
|
|
|
KEYWORD
|
nonn,base,fini
|
|
|
AUTHOR
|
M. F. Hasler, Oct 10 2019
|
|
|
STATUS
|
approved
|
| |
|
|
