|
|
A073531
|
|
Number of n-digit positive integers with all digits distinct.
|
|
8
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
For any base b the number of distinct-digit numbers is finite. For base 10, the maximal distinct-digit number is 9876543210; for any larger number at least two digits coincide. The number of distinct-digit primes is also finite, see A073532.
If "positive" is replaced by "nonnegative" we get the sequence 10, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, 3265920.
Alternatively, if 0 is considered to have 0 digits, one could prefix a(0) = 1. This would be compatible with the given formula and 9/10 rounded to the nearest integer. - M. F. Hasler, Dec 10 2018
a(10) is the final term because no number having more than 10 digits can have all digits distinct. - Jon E. Schoenfield, May 17 2021
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Digit
|
|
FORMULA
|
a(n) = 9*9!/(10-n)!.
|
|
EXAMPLE
|
a(3) = 648 because there are 648 three-digit integers with distinct digits.
|
|
MAPLE
|
seq(9*factorial(9)/(factorial(10-n)), n=1..10); # Muniru A Asiru, Dec 11 2018
|
|
MATHEMATICA
|
Table[9*9!/(10-n)!, {n, 10}]
|
|
PROG
|
(PARI) apply( A073531(n)=if(n<11, 9*9!\/(10-n)!), [1..13]) \\ or: 9*binomial(9, 10-n)*(n-1)! without need for if(). - M. F. Hasler, Dec 10 2018
(GAP) List([1..10], n->9*Factorial(9)/(Factorial(10-n))); # Muniru A Asiru, Dec 11 2018
(Magma) [9*Factorial(9)/Factorial(10-n): n in [1..10]]; // Vincenzo Librandi, Dec 13 2018
|
|
CROSSREFS
|
Cf. A010784 for the list of these integers.
|
|
KEYWORD
|
nonn,base,fini,full
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|