OFFSET
1,1
COMMENTS
This is a finite sequence with 9*9! = 3265920 terms: a(9*9!) = 9876543210.
A171102 is the infinite version, where each digit must appear at least once.
More precisely, this is exactly the subset of the first 9*9! terms of A171102. - M. F. Hasler, Jan 05 2020
A178788(a(n)) = 1. - Reinhard Zumkeller, Jun 30 2010
All these numbers are composite because the sum of the digits, 45, is divisible by 9. - T. D. Noe, Nov 09 2011
This is the 10th row of the array T(k,n) = n-th number in which the number of distinct base-10 digits is k. A031969 is the 4th row. A220063 is the 5th row. A220076 is the 6th row. A218019 is the 7th row. A219743 is the 8th row. - Jonathan Vos Post, Dec 05 2012
From Hieronymus Fischer, Feb 13 2013: (Start)
The sum of all terms is 9!*49444444440 = 17942399998387200.
General formula for the sum of all terms of the finite sequence of the corresponding base-p pandigital numbers with p places: sum = ((p^2 - p - 1)*(p^p - 1) + p - 1)*(p-2)!/2.
General formula for the sum of all terms (interpreted as decimal permutational numbers with exactly d+1 different digits from the range 0..d < 10): sum = (d+1)!*((10d - 1)*10^d - d + 1)/18, d > 1.
(End)
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Pandigital Number
Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
FORMULA
MATHEMATICA
Select[ FromDigits@# & /@ Permutations[ Range[0, 9]], # > 10^9 &, 20] (* Robert G. Wilson v, May 30 2010, Jan 17 2012 *)
PROG
(PARI) A050278(n)={ my(b=vector(9, k, 1+(n+9!-1)%(k+1)!\k!), t=b[9]-1, d=vector(9, i, i+(i>t)-1)); for(i=1, 8, t=10*t+d[b[9-i]]; d=vecextract(d, Str("^"b[9-i]))); t*10+d[1]} \\ M. F. Hasler, Jan 15 2012
(PARI) is_A050278(n)={ 9<#vecsort(Vecsmall(Str(n)), , 8) & n<1e10 } /* assuming that n is a nonnegative integer */ /* M. F. Hasler, Jan 10 2012 */
(PARI) a(n)=my(d=numtoperm(10, n+9!-1)); sum(i=1, #d, (d[i]-1)*10^(#d-i)) \\ David A. Corneth, Jun 01 2014
(Python)
from itertools import permutations
A050278_list = [int(''.join(d)) for d in permutations('0123456789', 10) if d[0] != '0'] # Chai Wah Wu, May 25 2015
CROSSREFS
KEYWORD
nonn,base,fini
AUTHOR
Eric W. Weisstein, Dec 11 1999
EXTENSIONS
Edited by N. J. A. Sloane, Sep 25 2010 to clarify that this is a finite sequence
STATUS
approved