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A076493
Number of common (distinct) decimal digits of n and n^2.
8
1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 1, 1, 1
OFFSET
0,11
COMMENTS
a(A029783(n)) = 0, a(A189056(n)) > 0; 0 <= a(n) <= 10, see example for first occurrences. [Reinhard Zumkeller, Apr 16 2011]
LINKS
EXAMPLE
a(2) = #{} = 0: 2^2 = 4;
a(0) = #{0} = 1: 0^2 = 0;
a(10) = #{0,1} = 2: 10^2 = 100;
a(105) = #{0,1,5} = 3: 105^2 = 11025;
a(1025) = #{0,1,2,5} = 4: 1025^2 = 1050625;
a(10245) = #{0,1,2,4,5} = 5: 10245^2 = 104960025;
a(102384) = #{0,1,2,3,4,8} = 6: 102384^2 = 10482483456;
a(1023456789) = #{0 .. 9} = 10: 1023456789^2 = 1047463798950190521.
MATHEMATICA
Table[Length[Intersection[IntegerDigits[n], IntegerDigits[n^2]]], {n, 1, 100}]
PROG
(Haskell)
import Data.List (intersect, nub)
import Data.Function (on)
a076493 n = length $ (intersect `on` nub . show) n (n^2)
-- Reinhard Zumkeller, Apr 16 2011
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Oct 21 2002
EXTENSIONS
Initial 1 added and offset adjusted by Reinhard Zumkeller, Apr 16 2011
STATUS
approved