A249587 - OEIS

%I #18 Dec 08 2018 03:28:28

%S 1,2,3,7,8,9,10,15,20,25,30,35,45,55,65,70,75,80,85,90,95,100,125,150,

%T 165,175,185,200,205,225,245,250,265,275,285,300,305,325,350,450,525,

%U 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

%N Numbers whose square remains square when the initial digit is removed.

%C The squares are in A225885.

%C 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.

%H Chai Wah Wu, <a href="/A249587/b249587.txt">Table of n, a(n) for n = 1..5000</a>

%t 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 *)

%t Sqrt[#]&/@Select[Range[2500]^2,IntegerQ[Sqrt[FromDigits[ Rest[ IntegerDigits[ #]]]]]&] (* _Harvey P. Dale_, May 01 2017 *)

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

%Y Cf. A225873. See also A227916.

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Nov 01 2014