|
|
A050278
|
|
Pandigital numbers: numbers containing the digits 0-9. Version 1: each digit appears exactly once.
|
|
83
|
|
|
1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976, 1023459678, 1023459687, 1023459768
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
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
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
|
|
|
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
|
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane, Sep 25 2010 to clarify that this is a finite sequence
|
|
STATUS
|
approved
|
|
|
|