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A050278 Pandigital numbers: numbers containing the digits 0-9. Version 1: each digit appears exactly once. 45
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.

Subsequence of A134336 and of A178403; A178401(a(n)) = 1. - Reinhard Zumkeller, May 27 2010

Smallest prime factors: A178775(n) = A020639(a(n)). - Reinhard Zumkeller, Jun 11 2010

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 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

FORMULA

A050278 = 9*A171571. - M. F. Hasler, Jan 12 2012

A050278(n) = A171102(n) for n <= 9*9!.

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

CROSSREFS

Cf. A171102, A050288, A050289.

Cf. A199630, A199631, A114260, A199632, A199633.

Cf. A031969, A050278, A220063, A220076, A218019, A219743.

Sequence in context: A204045 A061604 A171102 * A051018 A020667 A154566

Adjacent sequences:  A050275 A050276 A050277 * A050279 A050280 A050281

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

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Last modified October 1 00:26 EDT 2014. Contains 247498 sequences.