login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010784 Numbers with distinct decimal digits. 56
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 105, 106, 107, 108, 109, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

More than the usual number of terms are displayed in order to show the difference from some closely related sequences.

Also: a(1) = 0; a(n) = Min{x integer | x > a(n-1) and all digits to base 10 are distinct}.

This sequence is finite: a(8877691) = 9876543210 is the last term; a(8877690) = 9876543201. The largest gap between two consecutive terms before a(249999) = 2409653 is 104691, as a(175289) = 1098765, a(175290) = 1203456. - Reinhard Zumkeller, Jun 23 2001

Complement of A109303. - David Wasserman, May 21 2008

For the analogs in other bases b, search for "xenodromes."  A001339(b-1) is the number of base b xenodromes for b >= 2. - Rick L. Shepherd, Feb 16 2013

A073531 gives the number of positive n-digit numbers in this sequence. Note that it does not count 0. - T. D. Noe, Jul 09 2013

Can be seen as irregular table whose n-th row holds the n-digit terms; length of row n is then A073531(n) = 9*9!/(10-n)! except for n = 1 where we have 10 terms, unless 0 is considered to belong to a row 0. - M. F. Hasler, Dec 10 2018

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit

FORMULA

A178788(a(n)) = 1; A178787(a(n)) = n; A043537(a(n)) = A055642(a(n)). - Reinhard Zumkeller, Jun 30 2010

A107846(a(n)) = 0. - Reinhard Zumkeller, Jul 09 2013

MAPLE

A010784 := proc(q) local a, b, c, n;

  for n from 0 to q do a:=n; b:=[];

    while a>0 do c:=a mod 10; b:=[op(b), c]; a:=trunc(a/10); od;

    a:=nops(b); b:=nops({op(b)}); if a-b=0 then print(n); fi;

  od; end: A010784(10^4); # Paolo P. Lava, Apr 18 2013

MATHEMATICA

Select[Range[0, 100], Max[DigitCount[#]] == 1 &] (* Harvey P. Dale, Apr 04 2013 *)

PROG

(Haskell)

a010784 n = a010784_list !! (n-1)

a010784_list = filter ((== 1) . a178788) [1..]

-- Reinhard Zumkeller, Sep 29 2011

(PARI) is(n)=my(v=vecsort(digits(n))); v==vecsort(v, , 8) \\ Charles R Greathouse IV, Sep 17 2012

(PARI) select( is(n)=!n||#Set(digits(n))==logint(n, 10)+1, [0..120]) \\ M. F. Hasler, Dec 10 2018

(PARI) apply( A010784_row(n, L=List(if(n>1, [])))={forvec(d=vector(n, i, [0, 9]), forperm(d, p, p[1]&&listput(L, fromdigits(Vec(p)))), 2); Set(L)}, [1..2]) \\ A010784_row(n) returns all terms with n digits. - M. F. Hasler, Dec 10 2018

CROSSREFS

Subsequence of A043096.

Cf. A109303, A029743 (primes), A001339.

Sequence in context: A059543 A241158 A241157 * A052081 A031995 A023752

Adjacent sequences:  A010781 A010782 A010783 * A010785 A010786 A010787

KEYWORD

nonn,base,fini

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed to 1 and first comment adjusted by Reinhard Zumkeller, Jun 14 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 08:17 EST 2019. Contains 319210 sequences. (Running on oeis4.)