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Number of distinct-digit integers between squares.
0

%I #8 Mar 30 2012 17:26:02

%S 2,4,5,7,9,11,13,14,16,9,18,20,21,18,20,26,26,22,30,32,28,35,29,38,33,

%T 41,36,44,38,49,23,46,7,7,46,36,42,43,48,43,51,44,46,44,56,49,1,54,55,

%U 56,57,59,60,53,60,62,35,43,68,71,64,74,67,72,66,31,73,75,75,77,79,86

%N Number of distinct-digit integers between squares.

%C The number of distinct-digit integers is finite therefore the sequence contains only zeros after n=31427. The last nonzero terms are a(31420)=492, a(31421)=414, a(31422)=378, a(31423)=648, a(31424)=382, a(31425)=338, a(31426)=720 and a(31427)=0, a(31428)=0...

%e a(10)=9 because between 10^2 and 11^2 there are 9 integers with distinct digits: 102, 103, 104, 105, 106, 107, 108, 109, 120.

%t Table[Length[Select[Table[n, {n, x^2+1, (x+1)^2-1}], Length[IntegerDigits[ # ]]==Length[Union[IntegerDigits[ # ]]]&]], {x, 31428}]

%K nonn,base

%O 1,1

%A _Zak Seidov_, Sep 01 2002