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A073531 Number of n-digit positive integers with all distinct digits. 5
9, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, 3265920, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
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, 0, 0, 0, ...

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

LINKS

Table of n, a(n) for n=1..13.

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. A073532.

Cf. A010784 for the list of these integers.

Sequence in context: A272242 A206728 A206857 * A206694 A125910 A171283

Adjacent sequences:  A073528 A073529 A073530 * A073532 A073533 A073534

KEYWORD

base,nonn

AUTHOR

Zak Seidov, Aug 29 2002

STATUS

approved

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)