login
Numbers in which squares may end (in base 10).
4

%I #20 Feb 27 2015 23:26:44

%S 0,1,4,5,6,9,16,21,24,25,29,36,41,44,49,56,61,64,69,76,81,84,89,96,

%T 100,104,116,121,124,129,136,144,156,161,164,169,176,184,196,201,204,

%U 209,216,224,225,236,241,244,249,256,264,276,281,284,289,296,304

%N Numbers in which squares may end (in base 10).

%C The union of "squares mod 10" (= the first 6 terms) and "squares mod 100" (A010461) and "squares mod 1000" (A122986) etc.

%C The number of terms < 10^k beginning with k=0: 1, 6, 24, 165, 1101, 9306, 79620, 753462, 7198791, 70919559, ... - _Robert G. Wilson v_, Sep 04 2014

%H Derek Orr, <a href="/A238712/b238712.txt">Table of n, a(n) for n = 1..9306</a>

%F If n is present so is n^2. - _Robert G. Wilson v_, Sep 04 2014

%e 6 is in the sequence because 4^2 = 16 ends in the digit 6.

%e 7 is not in the sequence because no square can end with the digit 7.

%t mx = 3; t = Union@ Table[ Mod[n^2, 10^mx], {n, 10^mx/2}]; t = Union@ Flatten@ Table[ Mod[t, 10^m], {m, mx}] (* _Robert G. Wilson v_, Sep 04 2014 *)

%o (PARI) a=[];for(m=1,3,a=setunion(a,Set(vector(10^m,n,n^2)%10^m)));a

%Y Cf. A161355, A246422, A246448 (Complement).

%K nonn,base

%O 1,3

%A _M. F. Hasler_, Mar 03 2014