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A164782 Numbers k with property that average digit of k^2 is 3.

%I A164782 #16 Apr 11 2023 19:22:33
%S A164782 12,15,18,21,30,330,339,345,354,360,369,375,381,399,402,405,420,429,
%T A164782 453,459,462,465,468,471,489,492,495,498,504,540,552,555,558,561,570,
%U A164782 579,585,639,642,645,651,660,690,708,711,720,729,735,750,780,789,795,801
%N A164782 Numbers k with property that average digit of k^2 is 3.
%C A164782 All terms are multiples of 3.
%H A164782 Robert Israel, <a href="/A164782/b164782.txt">Table of n, a(n) for n = 1..10000</a>
%e A164782 a(1) = 12 because 12^2 = 144 and (1 + 4 + 4)/3 = 3.
%e A164782 a(53) = 801 because 801^2 = 641601 and (6 + 4 + 1 + 6 + 0 + 1)/6 = 3.
%p A164782 filter:= proc(n) local L;
%p A164782 L:= convert(n^2,base,10);
%p A164782 convert(L,`+`)=3*nops(L)
%p A164782 end proc:
%p A164782 select(filter, [seq(i,i=3..1000,3)]); # _Robert Israel_, Nov 01 2018
%t A164782 s={};Do[If[3==Mean[IntegerDigits[n^2]],Print[n];AppendTo[s,n]],{n,3,1000,3}];s
%t A164782 Select[Range[1000],Mean[IntegerDigits[#^2]]==3&] (* _Harvey P. Dale_, Jan 13 2015 *)
%o A164782 (GAP) Filtered([1..801],n->Sum(ListOfDigits(n^2))/Size(ListOfDigits(n^2))=3); # _Muniru A Asiru_, Nov 01 2018
%Y A164782 Subsequence of A164817.
%Y A164782 Average of digits of n^2 = s: A164771 (s=1), A164770 (s=2), A164782 (s=3), A164776 (s=4), A164774 (s=5), A164778 (s=6), A164773 (s=7), A164772 (s=8).
%K A164782 nonn,base
%O A164782 1,1
%A A164782 _Zak Seidov_, Aug 26 2009