A076493 -id:A076493 - cp's OEIS frontend

A043537 Number of distinct base-10 digits of n.

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

Offset: 1

Clark Kimberling

a(A000079(A130694(n))) = 10. - Reinhard Zumkeller, Jul 29 2007
a(A000290(A016070(n))) = 2. - Reinhard Zumkeller, Aug 05 2010
a(n) = 10 for almost all n. - Charles R Greathouse IV, Oct 02 2013

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

Cf. A047726, A118668, A119797, A119798, A119799, A119823, A038378, A076493, A055642, A178788.

import Data.List (nub)
a043537 = length . nub . show  -- Reinhard Zumkeller, Apr 16 2011

A043537 := proc(n)
        convert(convert(n,base,10),set) ;
        nops(%) ;
end proc: # R. J. Mathar, Dec 22 2012

Count[DigitCount@ #, n_ /; n > 0] & /@ Range@ 120 (* Michael De Vlieger, Aug 29 2015 *)

a(n)=#vecsort(digits(n),,8) \\ Charles R Greathouse IV, Oct 02 2013

def A043537(n): return len(set(str(n))) # Dimiter Skordev, Oct 02 2021

A029783 Exclusionary squares: numbers n such that no digit of n is present in n^2.

Original entry on oeis.org

2, 3, 4, 7, 8, 9, 17, 18, 22, 24, 29, 33, 34, 38, 39, 44, 47, 53, 54, 57, 58, 59, 62, 67, 72, 77, 79, 84, 88, 92, 94, 144, 157, 158, 173, 187, 188, 192, 194, 209, 212, 224, 237, 238, 244, 247, 253, 257, 259, 307, 313, 314, 333, 334, 338, 349, 353, 359

Offset: 1

Patrick De Geest

Complement of A189056; A076493(a(n)) = 0. - Reinhard Zumkeller, Apr 16 2011
A258682(a(n)) = a(n)^2. - Reinhard Zumkeller, Jun 07 2015
a(78) = 567 and a(112) = 854 are the only two numbers k such that the equation k^2 = m uses only once each of the digits 1 to 9 (reference David Wells). Exactly: 567^2 = 321489, and, 854^2 = 729316 (see A059930). - Bernard Schott, Jan 28 2021

			From _M. F. Hasler_, Oct 16 2018: (Start)
It is easy to construct infinite subsequences of the form S(a,b)(n) = a*R(n) + b, where R(n) = (10^n-1)/9 is the repunit of length n. Among these are:
S(3,0) = (3, 33, 333, ...), S(3,1) = (4, 34, 334, 3334, ...), S(3,5) = (8, 38, 338, ...), also b = 26, 44, 434, ... (with a = 3); S(6,1) = (7, 67, 667, ...), S(6,6) = (72, 672, 6672, ...) (excluding n=1), S(6,7) = (673, 6673, ...) (excluding also n=2 here), S(6,-7) = (59, 659, 6659, ...), and others. (End)

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, 1997, page 144, entry 567.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
Michael S. Branicky, Python program
Cliff Pickover et al, Exclusionary Squares and Cubes, rec.puzzles topic on google groups, January 2002

Cf. A059930 (n and n^2 use different digits), A112736 (numbers whose squares are exclusionary).

Cf. A029784, A029785, A029786, A111116, A113316, A189056, A076493, A258682.

a029783 n = a029783_list !! (n-1)
a029783_list = filter (\x -> a258682 x == x ^ 2) [1..]
-- Reinhard Zumkeller, Jun 07 2015, Apr 16 2011

Select[Range[1000], Intersection[IntegerDigits[ # ], IntegerDigits[ #^2]] == {} &] (* Tanya Khovanova, Dec 25 2006 *)

is_A029783(n)=!#setintersect(Set(digits(n)),Set(digits(n^2))) \\ M. F. Hasler, Oct 16 2018

Python
```
# see linked program
```

from itertools import count, islice
def A029783_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:not set(str(n))&set(str(n**2)),count(max(startvalue,0)))
A029783_list = list(islice(A029783_gen(),30)) # Chai Wah Wu, Feb 12 2023

Definition slightly reworded at the suggestion of Franklin T. Adams-Watters by M. F. Hasler, Oct 16 2018

A189056 Numbers having in decimal representation at least one common digit with their squares.

Original entry on oeis.org

0, 1, 5, 6, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 23, 25, 26, 27, 28, 30, 31, 32, 35, 36, 37, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 52, 55, 56, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 80, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

Offset: 1

Reinhard Zumkeller, Apr 16 2011

Complement of A029783; A076493(a(n)) > 0.

A258682(a(n)) < a(n)^2. - Reinhard Zumkeller, Jun 07 2015

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

Cf. A029783, A076493, A258682.

a189056 n = a189056_list !! (n-1)
a189056_list = 0 : filter (\x -> a258682 x /= x ^ 2) [1..]
-- Reinhard Zumkeller, Jun 07 2015, Apr 16 2011

Select[Range[0,120],Length[Intersection[IntegerDigits[#], IntegerDigits[ #^2]]]>0&] (* Harvey P. Dale, Aug 28 2012 *)

isok(n) = (n==0) || #setintersect(Set(digits(n)), Set(digits(n^2))); \\ Michel Marcus, Jun 13 2015

A109072 Number of decimal digits ( counted with multiplicity ) in n but not in n^2.

Original entry on oeis.org

0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 1, 1, 1, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1

Offset: 0

Zak Seidov, Jun 20 2005

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A076493 (number of common and distinct decimal digits of n and n^2).

Cf. A109071 (number of common decimal digits (counted with multiplicity) of n and n^2).

f:= proc(n) local L2;
L2:= convert(n^2,base,10);
nops(remove(t -> member(t,L2), convert(n,base,10)));
end proc:
map(f, [$0..200]); # Robert Israel, Feb 22 2017

UnsortedComplement[x_List, y__List]:=Replace[x, Dispatch[(#\[RuleDelayed]Sequence[])&/@Union[y]], 1]; Table[Length[UnsortedComplement[IntegerDigits[n], IntegerDigits[n^2]]], {n, 0, 200}]

A076494 Number of common decimal digits of 2^n and 2^(1+n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 2, 2, 3, 2, 1, 2, 3, 2, 1, 2, 2, 3, 4, 3, 2, 1, 1, 1, 4, 4, 5, 6, 6, 4, 3, 3, 5, 6, 6, 5, 4, 4, 5, 5, 5, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 5, 5, 6, 5, 7, 8, 7, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 7, 6, 7, 7, 8, 8, 8, 7, 9, 9, 8, 9, 9, 9, 9, 8, 9, 10, 10, 9, 7, 8, 8, 9, 10, 10, 10, 10, 9, 9, 10, 9

Offset: 1

Labos Elemer, Oct 21 2002

Cf. A006880, A076489-A076493.

Table[Length[Intersection[IntegerDigits[2^n], IntegerDigits[2^(n+1)]]], {n, 1, 100}]

A087773 Number of common decimal digits of n and 2^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 3, 3

Offset: 0

Reinhard Zumkeller, Oct 03 2003

Cf. A076493, A000079.

More terms from Ray Chandler, Oct 05 2003

A109073 Number of decimal digits ( counted with multiplicity ) in n^2 but not in n.

Original entry on oeis.org

0, 0, 1, 1, 2, 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2, 3, 3, 2, 1, 2, 3, 2, 3, 1, 1, 1, 2, 3, 1, 2, 3, 4, 4, 3, 3, 3, 4, 4, 2, 2, 3, 3, 4, 3, 3, 4, 3, 3, 1, 3, 3, 4, 4, 3, 3, 4, 4, 4, 1, 3, 4, 2, 2, 3, 3, 4, 3, 3, 2, 3, 4, 3, 2, 2, 1, 4, 3, 4, 2, 3, 3, 2, 4, 3, 3, 3, 4, 3, 2, 3, 4, 3, 4, 2, 2, 2, 3, 3, 0, 1, 2, 2, 2

Offset: 0

Zak Seidov, Jun 20 2005

Cf. A076493 Number of common and distinct decimal digits of n and n^2, A109071 Number of common decimal digits ( counted with multiplicity ) of n and n^2, A109072 Number of decimal digits ( counted with multiplicity ) in n but not in n^2.

			a(35)=4 because 34^2=1156 and there are 4 digits (counted with multiplicity) which are in 34^2 but not in 34.

Cf. A076493, A109071, A109072.

UnsortedComplement[x_List, y__List]:=Replace[x, Dispatch[(#\[RuleDelayed]Sequence[])&/@Union[y]], 1]; Table[Length[UnsortedComplement[IntegerDigits[n], IntegerDigits[n^2]]], {n, 0, 200}]

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A043537 Number of distinct base-10 digits of n.

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A029783 Exclusionary squares: numbers n such that no digit of n is present in n^2.

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A189056 Numbers having in decimal representation at least one common digit with their squares.

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Haskell

Mathematica

PARI

A109072 Number of decimal digits ( counted with multiplicity ) in n but not in n^2.

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Maple

Mathematica

A076494 Number of common decimal digits of 2^n and 2^(1+n).

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Mathematica

A087773 Number of common decimal digits of n and 2^n.

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Crossrefs

Extensions

A109073 Number of decimal digits ( counted with multiplicity ) in n^2 but not in n.

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Author

Keywords

Comments

Examples

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Programs

Mathematica