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A010784 Numbers with distinct decimal digits. 37
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}.

a 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

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

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

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

LINKS

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

Eric Weisstein's World of Mathematics, Digit

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

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

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.