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A010784 Numbers with distinct decimal digits. 86
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
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
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
(Python)
A010784_list = [n for n in range(10**6) if len(set(str(n))) == len(str(n))] # Chai Wah Wu, Oct 13 2019
(Python) # alternate for generating full sequence
from itertools import permutations
afull = [0] + [int("".join(p)) for d in range(1, 11) for p in permutations("0123456789", d) if p[0] != "0"]
print(afull[:100]) # Michael S. Branicky, Aug 04 2022
(Scala) def hasDistinctDigits(n: Int): Boolean = {
val numerStr = n.toString
val digitSet = numerStr.split("").toSet
numerStr.length == digitSet.size
}
(0 to 99).filter(hasDistinctDigits) // Alonso del Arte, Jan 09 2020
CROSSREFS
Subsequence of A043096.
Cf. A109303, A029740 (odds), A029741 (evens), A029743 (primes), A001339.
Sequence in context: A241157 A043096 A355301 * A052081 A031995 A023752
KEYWORD
nonn,base,fini
AUTHOR
EXTENSIONS
Offset changed to 1 and first comment adjusted by Reinhard Zumkeller, Jun 14 2010
STATUS
approved

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Last modified June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)