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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A225873. See also A227916.

Sequence in context: A037461 A284514 A268398 * A007607 A370902 A076682

Adjacent sequences: A249584 A249585 A249586 * A249588 A249589 A249590

Keyword

nonn,base

Author

M. F. Hasler, Nov 01 2014

Status

approved