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

0,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

A157466.

Sequence in context: A016500 A211451 A371809 * A046546 A189967 A139623

Adjacent sequences: A157461 A157462 A157463 * A157465 A157466 A157467

Keyword

base,nonn

Author

Reinhard Zumkeller, Mar 01 2009

Status

approved