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A157464 Number of distinct squares when inserting at most one digit in decimal representation of n. 3

%I #5 Sep 12 2021 19:30:36

%S 4,3,1,1,3,1,3,0,1,2,1,1,1,0,1,0,3,0,0,2,0,1,1,0,1,4,1,0,1,3,0,1,1,0,

%T 1,0,2,0,0,0,1,2,0,0,3,0,0,0,1,1,0,0,1,0,0,0,2,1,0,1,0,2,1,0,1,1,1,1,

%U 0,1,0,0,1,0,1,0,2,0,1,1,0,2,0,0,3,0,0,0,0,1,1,1,0,0,0,0,2,0,0,0,3,0,1,0,1

%N Number of distinct squares when inserting at most one digit in decimal representation of n.

%C a(A157465(n)) > 0; a(A000290(n)) > 0.

%H R. Zumkeller, <a href="/A157464/b157464.txt">Table of n, a(n) for n = 0..10000</a>

%e a(25) = #{25=5^2, 225=15^2, 256=16^2, 625=25^2} = 4;

%e a(26) = #{256=16^2} = 1;

%e a(27) = #{} = 0;

%e a(28) = #{289=17^2} = 1;

%e a(29) = #{289=17^2, 529=23^2, 729=27^2} = 3.

%t Join[{4},Table[Count[Union[Flatten[Table[FromDigits[Insert[IntegerDigits[n],d,m]],{d,0,9},{m,IntegerLength[n]+1}]]],_?(IntegerQ[Sqrt[#]]&)],{n,110}]] (* _Harvey P. Dale_, Sep 12 2021 *)

%Y A157466.

%K base,nonn

%O 0,1

%A _Reinhard Zumkeller_, Mar 01 2009

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Last modified September 5 14:14 EDT 2024. Contains 375699 sequences. (Running on oeis4.)