A043537 -id:A043537 - cp's OEIS frontend

A226778 Numbers having no common divisor > 1 with their reversal in decimal representation (see A043537).

1, 10, 13, 14, 16, 17, 19, 23, 25, 29, 31, 32, 34, 35, 37, 38, 41, 43, 47, 49, 52, 53, 56, 58, 59, 61, 65, 67, 71, 73, 74, 76, 79, 83, 85, 89, 91, 92, 94, 95, 97, 98, 100, 103, 104, 106, 107, 109, 112, 113, 115, 116, 118, 119, 122, 124, 125, 127, 128, 130

Offset: 1

Reinhard Zumkeller, Jun 18 2013

A055483(a(n)) = 1.

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

Cf. A043537, A055483, A071249 (complement).

a226778 n = a226778_list !! (n-1)
a226778_list = filter ((== 1) . a055483) [1..]

Select[Range[130], GCD[#, FromDigits[Reverse[IntegerDigits[#]]]] == 1 &] (* Jayanta Basu, Jul 24 2013 *)
Select[Range[150],Intersection[Divisors[#],Divisors[IntegerReverse[#]]] == {1}&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 07 2020 *)

isok(n) = gcd(n, subst(Pol(Vecrev(digits(n))), x, 10)) == 1; \\ Michel Marcus, Jul 02 2015

is(n)=gcd(fromdigits(Vecrev(digits(n))), n)==1 \\ Charles R Greathouse IV, Aug 25 2016

A055642 Number of digits in the decimal expansion of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Henry Bottomley, Jun 06 2000

From Hieronymus Fischer, Jun 08 2012: (Start)
For n > 0 the first differences of A117804.
The total number of digits necessary to write down all the numbers 0, 1, 2, ..., n is A117804(n+1). (End)
Here a(0) = 1, but a different common convention is to consider that the expansion of 0 in any base b > 0 has 0 terms and digits. - M. F. Hasler, Dec 07 2018

			Examples:
999: 1 + floor(log_10(999)) = 1 + floor(2.x) = 1 + 2 = 3 or
      ceiling(log_10(999+1)) = ceiling(log_10(1000)) = ceiling(3) = 3;
1000: 1 + floor(log_10(1000)) = 1 + floor(3) = 1 + 3 = 4 or
      ceiling(log_10(1000+1)) = ceiling(log_10(1001)) = ceiling(3.x) = 4;
1001: 1 + floor(log_10(1001)) = 1 + floor(3.x) = 1 + 3 = 4 or
      ceiling(log_10(1001+1)) = ceiling(log_10(1002)) = ceiling(3.x) = 4;

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Cf. A043537, A178788, A046034, A019546, A054899, A122840, A055640, A055641, A102669-A102685, A117804, A160093, A160094, A196563, A196564, A000120, A000788, A023416, A059015 (for base 2).
Cf. A262190, A262198.
Cf. A007953: sum of digits.

a055642 :: Integer -> Int
a055642 = length . show  -- Reinhard Zumkeller, Feb 19 2012, Apr 26 2011

[ #Intseq(n): n in [0..105] ];   //  Bruno Berselli, Jun 30 2011
(Common Lisp) (defun A055642 (n) (if (zerop n) 1 (floor (log n 10)))) ; James Spahlinger, Oct 13 2012

A055642 := proc(n)
        max(1,ilog10(n)+1) ;
end proc:  # R. J. Mathar, Nov 30 2011

Join[{1}, Array[ Floor[ Log[10, 10# ]] &, 104]] (* Robert G. Wilson v, Jan 04 2006 *)
Join[{1},Table[IntegerLength[n],{n,104}]]
IntegerLength[Range[0,120]] (* Harvey P. Dale, Jul 02 2016 *)

a(n)=#Str(n) \\ M. F. Hasler, Nov 17 2008

A055642(n)=logint(n+!n,10)+1 \\ Increasingly faster than the above, for larger n. (About twice as fast for n ~ 10^7.) - M. F. Hasler, Dec 07 2018

def a(n): return len(str(n))
print([a(n) for n in range(121)]) # Michael S. Branicky, May 10 2022

def A055642(n): # Faster than len(str(n)) from ~ 50 digits on
    L = math.log10(n or 1)
    if L.is_integer() and 10**int(L)>n: return int(L or 1)
    return int(L)+1  # M. F. Hasler, Apr 08 2024

a(A046760(n)) < A050252(A046760(n)); a(A046759(n)) > A050252(A046759(n)). - Reinhard Zumkeller, Jun 21 2011
a(n) = A196563(n) + A196564(n).
a(n) = 1 + floor(log_10(n)) = 1 + A004216(n) = ceiling(log_10(n+1)) = A004218(n+1), if n >= 1. - Daniel Forgues, Mar 27 2014
a(A046758(n)) = A050252(A046758(n)). - Reinhard Zumkeller, Jun 21 2011
a(n) = A117804(n+1) - A117804(n), n > 0. - Hieronymus Fischer, Jun 08 2012
G.f.: g(x) = 1 + (1/(1-x))*Sum_{j>=0} x^(10^j). - Hieronymus Fischer, Jun 08 2012
a(n) = A262190(n) for n < 100; a(A262198(n)) != A262190(A262198(n)). - Reinhard Zumkeller, Sep 14 2015

A010784 Numbers with distinct decimal digits.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Digit

Subsequence of A043096.

Cf. A109303, A029740 (odds), A029741 (evens), A029743 (primes), A001339.

a010784 n = a010784_list !! (n-1)
a010784_list = filter ((== 1) . a178788) [1..]
-- Reinhard Zumkeller, Sep 29 2011

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

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

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

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

A010784_list = [n for n in range(10**6) if len(set(str(n))) == len(str(n))] # Chai Wah Wu, Oct 13 2019

# 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

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

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

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

A047726 Number of different numbers that are formed by permuting digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 6

Offset: 1

N. J. A. Sloane

The minimum value of a(A171102(n)) is 10*9!. - Altug Alkan, Jul 08 2016

			From 102 we get 102, 120, 210, 201, 12 and 21, so a(102)=6.
From 33950 with 5 digits, one '0', two '3', one '5' and one '9', we get 5! / (1! * 2! * 1! * 1!) = 60 different numbers and a(33950) = 60.  - _Bernard Schott_, Oct 20 2019

A. Dunigan AtLee, Table of n, a(n) for n = 1..100000.

Cf. A055098. Identical to A043537 and A043562 for n<100.

Cf. A179239. - Aaron Dunigan AtLee, Jul 14 2010

import Data.List (permutations, nub)
a047726 n = length $ nub $ permutations $ show n
-- Reinhard Zumkeller, Jul 26 2011

f:= proc(n) local L;
  L:= convert(n,base,10);
  nops(L)!/mul(numboccur(i,L)!,i=0..9);
end proc:
map(f, [$1..1000]); # Robert Israel, Jul 08 2016

pd[n_]:=Module[{p=Permutations[IntegerDigits[n]]},Length[Union [FromDigits/@p]]]; pd/@Range[120]  (* Harvey P. Dale, Mar 22 2011 *)

a(n)=n=eval(Vec(Str(n)));(#n)!/prod(i=0,9,sum(j=1,#n,n[j]==i)!) \\ Charles R Greathouse IV, Sep 29 2011

A047726(n)={local(c=Vec(0,10)); apply(d->c[d+1]++, digits(n)); logint(n*10,10)!/prod(i=1,10,c[i]!)} \\ M. F. Hasler, Oct 18 2019

a(n) << n / (log_10 n)^4.5 by Stirling's approximation. - Charles R Greathouse IV, Sep 29 2011

a(n) = A000142(A055642(n))/Product_{k=0..9} A000142(A100910(n,k)). - Robert Israel, Jul 08 2016

Corrected by Henry Bottomley, Apr 19 2000

A178788 Characteristic function of numbers having distinct digits in their decimal representation.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1

Offset: 0

Reinhard Zumkeller, Jun 30 2010

a(A010784(n)) = 1; a(A109303(n)) = 0;
first differences of A178787.
a(n) <= A196368(n).
a(n) = 0 for n > 9*9!. - Hieronymus Fischer, Feb 02 2013

R. Zumkeller, Table of n, a(n) for n = 0..10000
Michael De Vlieger, Plot a(n) at (x,y) = (n mod 1000, -floor(n/1000)), n = 1..10^6, where black represents a(n) = 1 and white represents a(n) = 0.
Eric Weisstein's World of Mathematics, Digit
Index entries for characteristic functions

import Data.List (nub)
a178788 n = fromEnum $ nub (show n) == show n
-- Reinhard Zumkeller, Sep 25 2011

lst = {}; Do[If[Select[Tally[IntegerDigits[n]][[All, 2]], # > 1 &] == {}, AppendTo[lst, 1], AppendTo[lst, 0]], {n, 0, 104}]; lst (* Arkadiusz Wesolowski, May 10 2012 *)

a(n) = 0^(A055642(n)-A043537(n)).

A137580 Number of distinct digits in decimal representation of n!.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 6, 5, 6, 7, 5, 9, 8, 8, 9, 7, 7, 10, 9, 8, 9, 10, 8, 9, 9, 10, 9, 10, 10, 10, 10, 10, 9, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 0

Reinhard Zumkeller, Jan 27 2008

			n=12: 12! = 479001600 => a(12) = #{0,1,4,6,7,9} = 6.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for sequences related to factorial numbers.

Cf. A137577, A137578.

Cf. A034886.

import Data.List (nub, sort)
a137580 = length . nub . show . a000142
-- Reinhard Zumkeller, Apr 08 2012

Map[Length[Union[IntegerDigits[#]]] &, Table[n!, {n, 0, 79}]] (* Geoffrey Critzer, May 25 2013 *)

A137580(n)=#Set(digits(n!)) \\ M. F. Hasler, May 04 2015

a(n) = A043537(A000142(n)).
a(n) < 10 iff A137579(n) = 0.
a(A182049(n)) < 10. - Reinhard Zumkeller, Apr 08 2012

A031955 Numbers with exactly two distinct base-10 digits.

Original entry on oeis.org

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, 100, 101, 110, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 133, 141, 144, 151, 155, 161, 166

Offset: 1

Clark Kimberling

The three-digit terms are given by A210666(1,...,244). For numbers with exactly two distinct (but unspecified) digits in other bases, see A031948-A031954. For numbers made of two *given* digits, see A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9), and A032804-A032816 (in other bases). - M. F. Hasler, Apr 04 2015
A235154 is a subsequence. - Altug Alkan, Dec 03 2015
A235717 is a subsequence. - Robert Israel, Dec 03 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Different from A029742.

Cf. A043638, A101594, A031948, A031949, A031950, A031951, A031952, A031953, A031954, A235154, A235717.

a031955 n = a031955_list !! (n-1)
a031955_list = filter ((== 2) . a043537) [0..]
-- Reinhard Zumkeller, Feb 05 2012

M:= 5: # to get all terms < 10^M
sort([seq(seq(seq(seq(add(10^(m-j)*`if`(member(j,S2),d2,d1),j=1..m)  ,
  S2 = combinat:-powerset({$2..m}) minus {{}}),
  d2 = {$0..9} minus {d1}), d1 = 1..9), m=2..M)]); # Robert Israel, Dec 03 2015

Select[Range@ 166, Length@ Union@ IntegerDigits@ # == 2 &] (* Michael De Vlieger, Dec 03 2015 *)

is_A031955(n)=#Set(digits(n))==2 \\ M. F. Hasler, Apr 04 2015

def ok(n): return len(set(str(n))) == 2
print(list(filter(ok, range(167)))) # Michael S. Branicky, Oct 12 2021

A043537(a(n)) = 2. - Reinhard Zumkeller, Dec 03 2009

Name edited by Charles R Greathouse IV, Feb 13 2017

A095048 Number of distinct digits needed to write all positive divisors of n in decimal representation.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 1, 5, 2, 4, 3, 5, 2, 6, 2, 5, 4, 2, 3, 6, 3, 4, 5, 5, 3, 6, 2, 6, 2, 5, 4, 7, 3, 5, 3, 6, 2, 6, 3, 3, 5, 5, 3, 6, 4, 4, 4, 6, 3, 9, 2, 7, 5, 5, 3, 7, 2, 4, 6, 6, 4, 4, 3, 7, 5, 7, 2, 8, 3, 5, 5, 8, 2, 7, 3, 7, 6, 4, 3, 7, 4, 6, 6, 4, 3, 9, 4, 6, 3, 5, 3, 7, 3, 6, 3, 5, 2, 8

Offset: 1

Reinhard Zumkeller, May 28 2004

a(n) <= 10, a(A095050(n)) = 10.
a(A206159(n)) <= 2. - Reinhard Zumkeller, Feb 05 2012
Almost all (in the sense of natural density) terms of this sequence are equal to 10. - Charles R Greathouse IV, Nov 16 2022

			Set of divisors of n=10: {1,2,5,10}, therefore a(10) = #{0,1,2,5} = 4.
Set of divisors of n=16: {1,2,4,8,16}, therefore a(16)=#{1,2,4,6,8} = 5.

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

Cf. A095049, A095050, A043537.

Cf. A027750, A059436.

import Data.List (group, sort)
a095048 = length . group . sort . concatMap show . a027750_row
-- Reinhard Zumkeller, Feb 05 2012

A095048 := proc(n)
    local digset ;
    digset := {} ;
    for d in numtheory[divisors](n) do
        digset := digset union convert(convert(d,base,10),set) ;
    end do:
    nops(digset) ;
end proc:
seq(A095048(n),n=1..80) ; # R. J. Mathar, May 13 2022

a(n) = my(d = divisors(n), s = 0); for(i = 1, #d, v = digits(d[i]); for(j = 1, #v, s = bitor(s, 1<David A. Corneth, Nov 16 2022

from sympy import divisors
def a(n):
    s = set("1"+str(n))
    if len(s) == 10: return 10
    for d in divisors(n, generator=True):
        s |= set(str(d))
        if len(s) == 10: return 10
    return len(s)
print([a(n) for n in range(1, 99)]) # Michael S. Branicky, Nov 16 2022

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

A130694 Exponents of powers of 2 that contain all ten digits.

Original entry on oeis.org

68, 70, 79, 82, 84, 87, 88, 89, 94, 95, 96, 97, 98, 100, 101, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144

Offset: 1

Greg Dresden, Jul 10 2007

It is believed that every power of 2 beyond 2^86 contains the digit 0.

For k in {51,67,72,76,81,86}, 2^k contains all nonzero digits, but does not contain 0. - Dimiter Skordev, Oct 05 2021

			2^68 = 295147905179352825856.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A007377, A000079.

Complement of A130696.

A2 := {}; Do[If[Length[Union[ IntegerDigits[2^ n]]] == 10, A2 = Join[A2, {n}]], {n, 1, 200}]; Print[A2]
Select[Range[200],Min[DigitCount[2^#]]>0&] (* Harvey P. Dale, Aug 03 2019 *)

is_A130694(n)=9<#Set(Vec(Str(1<M. F. Hasler, Aug 25 2012

A043537(A000079(a(n))) = 10. - Reinhard Zumkeller, Jul 29 2007

a(n) = n + 91 for n >= 78 (conjectured). - Chai Wah Wu, Jan 27 2020

Displayed terms double-checked by M. F. Hasler, Aug 25 2012

cp's OEIS Frontend

A226778 Numbers having no common divisor > 1 with their reversal in decimal representation (see A043537).

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A055642 Number of digits in the decimal expansion of n.

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A010784 Numbers with distinct decimal digits.

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A047726 Number of different numbers that are formed by permuting digits of n.

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A178788 Characteristic function of numbers having distinct digits in their decimal representation.

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A137580 Number of distinct digits in decimal representation of n!.

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