A107846 Number of duplicate digits of n.

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

Offset

0,112

Comments

a(A010784(n)) = 0; a(A109303(n)) > 0. - Reinhard Zumkeller, Jul 09 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

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

Example

a(11) = 1 because 11 has two total decimal digits but only one distinct digit (1) and 2-1=1.
Similarly, a(3653135) = 7 (total digits) - 4 (distinct digits: 1,3,5,6) = 3 (There are three duplicate digits here, namely, 3, 3 and 5).

Mathematica

Table[Total[Select[DigitCount[n]-1, #>0&]], {n, 0, 120}] (* Harvey P. Dale, Jul 31 2013 *)

Prog

(Haskell)
import Data.List (sort, group)
a107846 = length . concatMap tail . group . sort . show :: Integer -> Int
-- Reinhard Zumkeller, Jul 09 2013
(Python)
def a(n): return len(s:=str(n)) - len(set(s))
print([a(n) for n in range(105)]) # Michael S. Branicky, Jan 09 2023

Crossrefs

Cf. A055642 (Total decimal digits of n), A043537 (Distinct decimal digits of n).

Sequence in context: A355444 A070109 A355454 * A354983 A179801 A374093

Adjacent sequences: A107843 A107844 A107845 * A107847 A107848 A107849

Keyword

base,easy,nonn

Author

Rick L. Shepherd, May 24, 2005

Status

approved