A249587 Numbers whose square remains square when the initial digit is removed.

1, 2, 3, 7, 8, 9, 10, 15, 20, 25, 30, 35, 45, 55, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 165, 175, 185, 200, 205, 225, 245, 250, 265, 275, 285, 300, 305, 325, 350, 450, 525, 550, 575, 650, 700, 750, 775, 800, 850, 900, 945, 950, 975, 985, 1000, 1025, 1250, 1425, 1500, 1650, 1750, 1825, 1850, 2000, 2050, 2225, 2250, 2450, 2500

Offset: 1

Author

M. F. Hasler, Nov 01 2014

Keywords

• nonn
• base

Comments

The squares are in A225885.

The first three terms have a single-digit square which by convention yields 0 if the first digit is removed. The first 6 terms are the only terms of the sequence not divisible by 5.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A225873. See also A227916.

Programs

Mathematica

b /. Flatten[Outer[Solve[a^2 + #2*10^#1 == b^2 && 0 <= a < Sqrt[10^#1] && Sqrt[#2*10^#1] <= b < Sqrt[10^(#1 + 1)], {a, b}, Integers] &, Range[0, 5], Range[9]], 2] (* Davin Park, Dec 30 2016 *)
Sqrt[#]&/@Select[Range[2500]^2,IntegerQ[Sqrt[FromDigits[ Rest[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, May 01 2017 *)

PARI

is(n)=issquare(n^2%10^(#Str(n^2)-1))