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

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Mar 01 2009

Keywords

• base
• nonn

Comments

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

Examples

			a(25) = #{25=5^2, 225=15^2, 256=16^2, 625=25^2} = 4;
a(26) = #{256=16^2} = 1;
a(27) = #{} = 0;
a(28) = #{289=17^2} = 1;
a(29) = #{289=17^2, 529=23^2, 729=27^2} = 3.
		

Links

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

Crossrefs

A157466.

Programs

Mathematica

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 *)