A010784 -id:A010784 - cp's OEIS frontend

A247813 Numbers in decimal representation with distinct digits, such that in Spanish their digits are in alphabetic order.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 23, 26, 27, 28, 29, 31, 41, 42, 43, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 63, 67, 71, 73, 81, 83, 86, 87, 91, 93, 96, 97, 98, 231, 261, 263, 267, 271, 273, 281, 283, 286, 287, 291, 293, 296, 297, 298, 421, 423

Offset: 1

Reinhard Zumkeller, Oct 05 2014

List of decimal digits, alphabetically sorted by their names in Spanish:
0  cero, 5  cinco, 4  cuatro, 2  dos, 9  nueve, 8  ocho, 6  seis, 7  siete, 3  tres, 1  uno/una;
finite sequence with last and largest term a(512) = 542986731.

Reinhard Zumkeller, Table of n, a(n) for n = 1..512
Wikipedia, Zahlen in unterschiedlichen Sprachen
Wikipedia, List of numbers in various languages

Intersection of A010784 and A161390 .

Cf. A247800 (Czech), A247801 (Danish), A247802 (Dutch), A053433 (English), A247803 (Finnish), A247804 (French), A247805 (German), A247806 (Hungarian), A247807 (Italian), A247808 (Latin), A247809 (Norwegian), A247810 (Polish), A247807 (Portuguese), A247811 (Russian), A247812 (Slovak), A247809 (Swedish), A247814 (Turkish).

import Data.IntSet (fromList, deleteFindMin, union)
import qualified Data.IntSet as Set (null)
a247813 n = a247813_list !! (n-1)
a247813_list = 0 : f (fromList [1..9]) where
   f s | Set.null s = []
       | otherwise  = x : f (s' `union`
         fromList (map (+ 10 * x) $ tail $ dropWhile (/= mod x 10) digs))
       where (x, s') = deleteFindMin s
   digs = [0, 5, 4, 2, 9, 8, 6, 7, 3, 1]

A247814 Numbers in decimal representation with distinct digits, such that in Turkish their digits are in alphabetic order.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 17, 18, 19, 20, 23, 27, 28, 37, 40, 42, 43, 47, 48, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 80, 83, 87, 90, 92, 93, 94, 97, 98, 103, 107, 120, 123, 127, 128, 137, 140, 142, 143, 147

Offset: 1

Reinhard Zumkeller, Oct 05 2014

List of decimal digits, alphabetically sorted by their names in Turkish:
6  altı, 5  beş, 1  bir, 9  dokuz, 4  dört, 2  iki, 8  sekiz, 0  sıfır, 3  üç, 7  yedi;
finite sequence with last and largest term a(1020) = 6519428037.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1020
Wikipedia, Zahlen in unterschiedlichen Sprachen
Wikipedia, List of numbers in various languages

Intersection of A010784 and A247764.

Cf. A247800 (Czech), A247801 (Danish), A247802 (Dutch), A053433 (English), A247803 (Finnish), A247804 (French), A247805 (German), A247806 (Hungarian), A247807 (Italian), A247808 (Latin), A247809 (Norwegian), A247810 (Polish), A247807 (Portuguese), A247811 (Russian), A247812 (Slovak), A247813 (Spanish), A247809 (Swedish).

import Data.IntSet (fromList, deleteFindMin, union)
import qualified Data.IntSet as Set (null)
a247814 n = a247814_list !! (n-1)
a247814_list = 0 : f (fromList [1..9]) where
   f s | Set.null s = []
       | otherwise  = x : f (s' `union`
         fromList (map (+ 10 * x) $ tail $ dropWhile (/= mod x 10) digs))
       where (x, s') = deleteFindMin s
   digs = [6, 5, 1, 9, 4, 2, 8, 0, 3, 7]

A109303 Numbers k with at least one duplicate base-10 digit (A107846(k) > 0).

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166, 171, 177, 181, 188, 191, 199, 200, 202, 211, 212, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 232, 233, 242

Offset: 1

Rick L. Shepherd, Jun 24 2005

Complement of A010784, numbers with distinct base-10 digits, so all numbers greater than 9876543210 (last term of A010784) are terms. a(263)=1001 is the first term not also a term of A044959; a(264)=1002 is the first term not also a term of A084050. The terms of A044959 greater than 9 are a subsequence. The terms of A084050 greater than 90 are a subsequence.
A178788(a(n)) = 0; A178787(a(n)) = A178787(a(n)-1); A043537(a(n)) < A109303(a(n)). - Reinhard Zumkeller, Jun 30 2010
A227362(a(n)) < a(n). - Reinhard Zumkeller, Jul 09 2013

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A010784 (numbers with distinct digits), A044959 (numbers with no two equally numerous digits), A084050 (numbers with a palindromic permutation of digits), A107846 (number of duplicate digits of n). Also see A062813, which gives the largest number in each base containing all distinct digits.

a109303 n = a109303_list !! (n-1)
a109303_list = filter ((> 0) . a107846) [0..]
-- Reinhard Zumkeller, Jul 09 2013

Select[Range[300], Max[DigitCount[#]] > 1 &] (* Harvey P. Dale, Jan 14 2011 *)

def ok(n): s = str(n); return len(set(s)) < len(s)
print([k for k in range(243) if ok(k)]) # Michael S. Branicky, Nov 22 2021

A320485 Keep just the digits of n that appear exactly once; write -1 if all digits disappear.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, -1, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, -1, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, -1, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, -1, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, -1, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, -1, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, -1, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, -1, 1, 0, 102, 103, 104, 105, 106, 107, 108, 109, 0, -1, 2, 3, 4, 5, 6, 7, 8, 9, 120, 2, 1, 123, 124, 125, 126, 127, 128, 129, 130, 3

Offset: 0

N. J. A. Sloane, Oct 24 2018

Digits that appear more than once in n are erased. Leading zeros are erased unless the result is 0. If all digits are erased, we write -1 for the result.
The map n -> a(n) was invented by Eric Angelini and described in a posting to the Sequence Fans Mailing List on Oct 24 2018.
More than the usual number of terms are shown in order to reach some interesting examples.
a(n) = -1 mostly. - David A. Corneth, Oct 24 2018

			1231 becomes 23, 1123 becomes 23, 11231 becomes 23, and 11023 becomes 23 (as we don't accept leading zeros). Note that 112323 disappears immediately and we get -1.
101 and 110 become 0 while 11000 and 10001 become -1.

Eric Angelini, Posting to Sequence Fans Mailing List, Oct 24 2018

Robert Israel, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

See A320486 for another version.

Cf. A010784, A115853, A321008-A321012.

f:= proc(n) local F,S;
  F:= convert(n,base,10);
  S:= select(t -> numboccur(t,F)>1, [$0..9]);
  if S = {} then return n fi;
  F:= subs(seq(s=NULL,s=S),F);
  if F = [] then -1
  else add(F[i]*10^(i-1),i=1..nops(F))
  fi
end proc:
map(f, [$0..200]); # Robert Israel, Oct 24 2018

Array[If[# == {}, -1, FromDigits@ #] &@ Map[If[#[[-1]] > 1, -1, #[[1]] ] /. -1 -> Nothing &, Tally@ IntegerDigits[#]] &, 131] (* Michael De Vlieger, Oct 24 2018 *)

a(n) = {my(d=digits(n), v = vector(10), res = 0, t = 0); for(i=1, #d, v[d[i]+1]++); for(i=1, #d, if(v[d[i]+1]==1, t = 1; res=10 * res + d[i])); res - !t + !n} \\ David A. Corneth, Oct 24 2018

def A320485(n):
    return (lambda x: int(x) if x != '' else -1)(''.join(d if str(n).count(d) == 1 else '' for d in str(n))) # Chai Wah Wu, Nov 19 2018

From Rémy Sigrist, Oct 24 2018: (Start)
a(n) = n iff n belong to A010784.
a(n) <= 9876543210 with equality iff n = 9876543210.
(End)
If n > 9876543210, then a(n) < n. If a(n) < n, then a(n) <= 99n/1000. - Chai Wah Wu, Oct 24 2018

A154566 Smallest 10-digit number whose n-th power contains each digit (0-9) n times, or -1 if no such number exists.

Original entry on oeis.org

1023456789, 3164252736, 4642110594, 5623720662, 6312942339, 6813614229, 7197035958, 7513755246, 7747685775, 7961085846, 8120306331, 8275283289, 8393900487, 8626922994, 8594070624, 8691229761, 8800389678, 8807854905, 9873773268, 8951993472, 9473643936, 9585032094

Offset: 1

Zhining Yang, Jan 12 2009, Jan 13 2009

A number with 10*n digits could contain all ten digits(0-9) n times. The probability of this is (10n)!/((n!)^10 * 10^((10*n)-10^(10*n-1)). There are 10^10-10^(10-1/n)) numbers which are n-th powers of some 10-digit numbers. So there are about (10n)!*(10^10-10^(10-1/n)))/((n!)^10 * 10^((10*n)-10^(10*n-1)) numbers which satisfy the requirements.
Fortunately, I found a larger number than those shown here, for n=26, a(n)=9160395852. Since (10n)!*(10^10-10^(10-1/n))/((n!)^10 * 10^((10*n)-10^(10*n-1)) = 0.31691419..., this is a lucky event!
The sequence is -1 beyond a certain point because when n > 23025850928 we have 9999999999^n < 10^(10*n-1), i.e., it is impossible to obtain a power with 10*n digits. From a(23) to a(600) the only terms which are not -1 are a(24)=9793730157, a(26)=9160395852, a(35)=9959167017, and a(38)=9501874278. - Giovanni Resta, Jan 17 2020

			For n=18, a(n)=8807854905. That means 8807854905^18 has all digits 0-9 each 18 times and 8807854905 is the smallest 10-digit number which has this property.

Zhining Yang, Smallest Ten Digit Powers
Zhining Yang, Largest Ten Digit Powers

Cf. A010784, A078255, A154532.

def flag(p, n):
    for i in range(10):
        if not p.count(str(i)) == n:
            return False
    return True
def a(n):
    for i in range(3*int(10**(10-1/n)/3), 10**10, 3):
        if flag(str(i**n), n):
            return i
for i in range(1, 41):
    print(a(i), end=", ") # Zhining Yang, Oct 05 2022

Function Flag(ByVal s As String, ByVal num As Long) As Long
Dim b&(9), t&, i&
Flag = 1
If Len(s) <> 10 * num Then
    Flag = 0
    Exit Function
End If
For i = 1 To Len(s)
    t = Val(Mid(s, i, 1))
    b(t) = b(t) + 1
    If b(t) > num Then
        Flag = 0
        Exit Function
    End If
Next
End Function
'
Function Mypower(ByVal num As Currency, ByVal power As Long) As String
Dim b(), temp, i&, j&
ReDim b(1 To 2 * power)
ReDim s(1 To 2 * power)
b(2 * power - 1) = Val(Left(num, 5))
b(2 * power) = Val(Right(num, 5))
For i = 2 To power
    temp = 0
    For j = 2 * power To 1 Step -1
        temp = b(j) * num + temp
        b(j) = Format(Val(Right(temp, 5)), "00000")
        temp = Int(temp / 10 ^ 5)
    Next
Next
Mypower = Join(b, "")
End Function
'
Function a(ByVal n As Long)
Dim j As Currency, s As String, num&
For j = 3 * Int(1 + 10 ^ (10 - 1 / n) / 3) To 9999999999# Step 3
    DoEvents
    If Flag(Mypower(j, n), n) = 1 Then
        a = j
        Exit Function
    End If
Next
End Function ' Zhining Yang, Oct 11 2022

Edited by N. J. A. Sloane, Jan 13 2009
Edited by Charles R Greathouse IV, Nov 01 2009
Further edits by M. F. Hasler, Oct 05 2012
a(19)-a(22) from Giovanni Resta, Jan 17 2020
Added escape clause to definition. - N. J. A. Sloane, Nov 22 2022

A115569 Lynch-Bell numbers: numbers n such that the digits are all different (and do not include 0) and n is divisible by each of its individual digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 36, 48, 124, 126, 128, 132, 135, 162, 168, 175, 184, 216, 248, 264, 312, 315, 324, 384, 396, 412, 432, 612, 624, 648, 672, 728, 735, 784, 816, 824, 864, 936, 1236, 1248, 1296, 1326, 1362, 1368, 1395, 1632, 1692, 1764, 1824

Offset: 1

Mike Smith (mtm_king(AT)yahoo.com), Mar 10 2006; also submitted by Andy Edwards (AndynGen(AT)aol.com), Mar 20 2006

This is a subset of some of the related sequences listed below. Stephen Lynch and Andrew Bell are Brisbane surgeons who contributed to the identification of this sequence.
There are 548 Lynch-Bell numbers. A117911 gives the number of n-digit ones. The digit 5 cannot appear in Lynch-Bell numbers containing an even digit; 5 must be the units digit when it appears. The 7-digit Lynch-Bell numbers are 105 permutations of 1289736 (the smallest such). - Rick L. Shepherd, Apr 01 2006
Can be seen/read as a table with row lengths A117911 (rows r > 7 have zero length). - M. F. Hasler, Jan 31 2016

			384/3 = 128, 384/8 = 48, 384/4 = 96. Thus 384 is Lynch-Bell as it is a multiple of each of its three distinct digits.

Rick L. Shepherd, List of all terms

Cf. A034838, A034709, A063527.

Cf. A117911, A117912 (have even digits only), A117913 (have odd digits only), A010784.

with(combinat):
f:= l-> parse(cat(l[])):
T:= n-> sort(map(f, select(l-> andmap(x-> irem(f(l), x)=0, l),
         map(p-> permute(p)[], choose([$1..9], n)))))[]:
seq(T(n), n=1..7);  # Alois P. Heinz, Jul 31 2022

Reap[For[n = 1, n < 10^7, n++, id = IntegerDigits[n]; If[FreeQ[id, 0] && Length[id] == Length[Union[id]] && And @@ (Divisible[n, #]& /@ id), Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Nov 26 2013 *)
bnQ[n_]:=Max[DigitCount[n]]==1&&FreeQ[IntegerDigits[n],0]&&Union[Divisible[n,IntegerDigits[ n]]]=={True}; Select[Range[2000],lbnQ] (* Harvey P. Dale, Jun 02 2023 *)
Cases[Union @@ ((FromDigits@#&/@Flatten[Permutations@# & /@ Subsets[Range@9, {#}], 1])&/@ Range@9), ?(DeleteDuplicates[Divisible[#, IntegerDigits@#]] == {True} &)] (* _Hans Rudolf Widmer, Aug 27 2024 *)

A115569_row(n)={if(n,my(u=vectorv(n,i,10^i)\10,S=List(),M);forvec(v=vector(n,i,[1,9]),(M=lcm(v))%10==0||normlp(v,1)%3^valuation(M,3)||for(k=1,n!,vecextract(v,numtoperm(n,k))*u%M ||listput(S,vecextract(v,numtoperm(n,k))*u)),2);Set(S),concat(apply(A115569_row,[1..7])))} \\ Return terms of length n if given, else the vector of all terms. The checks M%10 and |v| % 3^v(...) are not needed but reduce CPU time by 97%. - M. F. Hasler, Jan 31 2016

A115569(n)=n>9&&for(r=2,7,(n-=#t=A115569_row(r))>9||return(t[n-9+#t]));n \\ M. F. Hasler, Jan 31 2016

def ok(n):
    s = str(n)
    if "0" in s or len(set(s)) < len(s): return False
    return all(n%int(d) == 0 for d in s)
afull = [k for k in range(9867313) if ok(k)]
print(afull[:55]) # Michael S. Branicky, Jul 31 2022

The full list of terms was sent in by Rick L. Shepherd (see link) and also by Sébastien Dumortier, Apr 04 2006

A154532 a(n) is the largest 10-digit number whose n-th power contains each digit (0-9) n times, or -1 no such number exists.

Original entry on oeis.org

9876543210, 9994363488, 9999257781, 9999112926, 9995722269, 9999409158, 9998033316, 9993870774, 9986053188, 9964052493, 9975246786, 9966918135, 9938689137, 9998781633, 9813743148, 9970902252, 9740383767, 9829440591, 9873773268, 9985819785, 9766102146, 9863817738

Offset: 1

Zhining Yang, Jan 11 2009

A number with 10*n digits may have all ten digits (0-9) repeated n times. The probability of this is (10n)!/((n!)^10 * 10^((10*n)-10^(10*n-1)). There are 10^10-10^(10-1/n)) numbers which are n-th powers of 10-digit numbers. So there may exist Count=(10n)!*(10^10-10^(10-1/n)))/((n!)^10 * 10^((10*n)-10^(2*n-1)) numbers with the desired property.

From a(23) to a(110) the only terms which exist are a(24)=9793730157, a(26)=9347769564, a(35)=9959167017, and a(38)=9501874278. (The other values of a(n) are -1.) - Zhining Yang, Oct 05 2022

			a(18) = 9829440591, so each digit (0-9) appears 18 times in the decimal expansion of 9829440591^18.

northwolves et al., Ten Digit Numbers
Zhining Yang, Largest Ten Digit Powers

Cf. A010784, A078255, A154566.

def flag(p, n):
    b = True
    for i in range(10):
        if not p.count(str(i)) == n:
            b = False
            break
    return b
def a(n):
    for i in range(10 ** 10 - 1, 3 * int(10 ** (10 - 1 / n) / 3), -3):
        p = str(i ** n)
        if flag(p, n) == True:
            return i
            break
for i in range(1, 23):
    print(i, a(i))  # Zhining Yang, Oct 10 2022

def flag(p, n):
    return all(p.count(d) == n for d in "0123456789")
def a(n):
    return next(i for i in range(10**10-1,3*int(10**(10-1/n)/3), -3) if flag(str(i**n), n))
for i in range(2, 23):
    print(i,a(i))  # Michael_S._Branicky, Oct 10 2022

Edited by N. J. A. Sloane, Jan 12 2009
a(19)-a(22) from Zhining Yang, Oct 05 2022
Definition revised by N. J. A. Sloane, Nov 22 2022

A073531 Number of n-digit positive integers with all digits distinct.

Original entry on oeis.org

9, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, 3265920

Offset: 1

Zak Seidov, Aug 29 2002

For any base b the number of distinct-digit numbers is finite. For base 10, the maximal distinct-digit number is 9876543210; for any larger number at least two digits coincide. The number of distinct-digit primes is also finite, see A073532.
If "positive" is replaced by "nonnegative" we get the sequence 10, 81, 648, 4536, 27216, 136080, 544320, 1632960, 3265920, 3265920.
Alternatively, if 0 is considered to have 0 digits, one could prefix a(0) = 1. This would be compatible with the given formula and 9/10 rounded to the nearest integer. - M. F. Hasler, Dec 10 2018
a(10) is the final term because no number having more than 10 digits can have all digits distinct. - Jon E. Schoenfield, May 17 2021

			a(3) = 648 because there are 648 three-digit integers with distinct digits.

Eric Weisstein's World of Mathematics, Digit

Cf. A073532.

Cf. A010784 for the list of these integers.

List([1..10],n->9*Factorial(9)/(Factorial(10-n))); # Muniru A Asiru, Dec 11 2018

[9*Factorial(9)/Factorial(10-n): n in [1..10]]; // Vincenzo Librandi, Dec 13 2018

seq(9*factorial(9)/(factorial(10-n)),n=1..10); # Muniru A Asiru, Dec 11 2018

Mathematica
```
Table[9*9!/(10-n)!, {n, 10}]
```

apply( A073531(n)=if(n<11,9*9!\/(10-n)!), [1..13]) \\ or: 9*binomial(9,10-n)*(n-1)! without need for if(). - M. F. Hasler, Dec 10 2018

a(n) = 9*9!/(10-n)!.

Keywords fini, full added by Jon E. Schoenfield, May 17 2021

A137564 a(n) is the number formed by removing from n all duplicate digits except the leftmost copy of each.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 4, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 5, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 6, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 7, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 8, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 9, 10, 10, 102, 103, 104, 105, 106, 107, 108, 109, 10, 1, 12

Offset: 0

Rick L. Shepherd, Jan 25 2008

Differs from A106612: a(100) = 10, A106612(100) = 100.
Differs from A337864: a(101) = 10, A337864(101) = 101.
a(n)=n iff n is a term of A010784. a(n)A109303.
A010784 is the sequence of distinct terms in this sequence, thus 9876543210 is the largest term here also, as no digit occurs more than once in any given term. Each term except 0 appears infinitely often in this sequence. - Rick L. Shepherd, Oct 03 2020

			a(100)=10 as a (second) 0 digit is dropped. a(1211323171)=1237.
a(10...1) = 10 for any number of 0's and/or 1's in any order replacing the "..." in the term's index. - _Rick L. Shepherd_, Oct 03 2020

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (corrected by Andrew Howroyd at the suggestion of Rodolfo Kurchan and Omar E. Pol, Oct 04 2020)

Cf. A106612, A010784 (fixed points), A109303 (non-fixed).

Cf. A043529 (equivalent in binary, except at n=0), A337864.

Table[FromDigits@ DeleteDuplicates@ IntegerDigits@ n, {n, 74}] (* Michael De Vlieger, Jun 01 2016 *)

a(n)={my(d=digits(n)); fromdigits(vecextract(d, vecsort(vecsort(d,,9))))} \\ Andrew Howroyd, Oct 04 2020

sub a {my($n)=@; my @seen; $n =~ s{.}{!$seen[$&]++ && $&}eg; $n} # _Kevin Ryde, Oct 04 2020

def a(n):
    seen, out, s = set(), "", str(n)
    for d in s:
        if d not in seen: out += d; seen.add(d)
    return int(out)
print([a(n) for n in range(113)]) # Michael S. Branicky, Jul 23 2022

A280593 Natural numbers whose digits can be formed by typing adjacent keys on a 123-456-789 keypad without repeating a digit.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 21, 23, 25, 32, 36, 41, 45, 47, 52, 54, 56, 58, 63, 65, 69, 74, 78, 85, 87, 89, 96, 98, 123, 125, 145, 147, 214, 236, 254, 256, 258, 321, 325, 365, 369, 412, 452, 456, 458, 478, 521, 523, 541, 547, 563, 569, 587, 589, 632, 652, 654, 658, 698, 741, 745, 785, 789

Offset: 1

FUNG Cheok Yin, Jan 06 2017

A subsequence of A010784. - FUNG Cheok Yin, Jul 05 2018

			The keypad is:
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
It is visibly obvious that 2589 can be formed on the keypad.

FUNG Cheok Yin, Table of n, a(n) for n = 1..653
FUNG Cheok Yin, C++ program

Cf. A010784, A280594, A280595.

g = Graph[{1 <-> 2, 1 <-> 4,
    2 <-> 1, 2 <-> 3, 2 <-> 5,
    3 <-> 2, 3 <-> 6,
    4 <-> 1, 4 <-> 5, 4 <-> 7,
    5 <-> 2, 5 <-> 4, 5 <-> 6, 5 <-> 8,
    6 <-> 3, 6 <-> 5, 6 <-> 9,
    7 <-> 4, 7 <-> 8,
    8 <-> 5, 8 <-> 7, 8 <-> 9,
    9 <-> 6, 9 <-> 8}];
f[{a_, b_}] := FindPath[g, a, b, Infinity, All]
ff = f /@ Flatten[Outer[List, r = Range[9], r], 1];
A280593 = Sort[Join[r, FromDigits /@ Flatten[ff, 1]]] (* Jean-François Alcover, Jan 06 2017 *)

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A247813 Numbers in decimal representation with distinct digits, such that in Spanish their digits are in alphabetic order.

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A247814 Numbers in decimal representation with distinct digits, such that in Turkish their digits are in alphabetic order.

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A109303 Numbers k with at least one duplicate base-10 digit (A107846(k) > 0).

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A320485 Keep just the digits of n that appear exactly once; write -1 if all digits disappear.

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A154566 Smallest 10-digit number whose n-th power contains each digit (0-9) n times, or -1 if no such number exists.

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A115569 Lynch-Bell numbers: numbers n such that the digits are all different (and do not include 0) and n is divisible by each of its individual digits.

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A154532 a(n) is the largest 10-digit number whose n-th power contains each digit (0-9) n times, or -1 no such number exists.

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