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

12, 15, 18, 21, 30, 330, 339, 345, 354, 360, 369, 375, 381, 399, 402, 405, 420, 429, 453, 459, 462, 465, 468, 471, 489, 492, 495, 498, 504, 540, 552, 555, 558, 561, 570, 579, 585, 639, 642, 645, 651, 660, 690, 708, 711, 720, 729, 735, 750, 780, 789, 795, 801

Offset: 1

Author

Zak Seidov, Aug 26 2009

Keywords

• nonn
• base

Comments

All terms are multiples of 3.

Examples

			a(1) = 12 because 12^2 = 144 and (1 + 4 + 4)/3 = 3.
a(53) = 801 because 801^2 = 641601 and (6 + 4 + 1 + 6 + 0 + 1)/6 = 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A164817.

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).

Programs

GAP

Filtered([1..801],n->Sum(ListOfDigits(n^2))/Size(ListOfDigits(n^2))=3); # Muniru A Asiru, Nov 01 2018

Maple

filter:= proc(n) local L;
L:= convert(n^2,base,10);
convert(L,`+`)=3*nops(L)
end proc:
select(filter, [seq(i,i=3..1000,3)]); # Robert Israel, Nov 01 2018

Mathematica

s={};Do[If[3==Mean[IntegerDigits[n^2]],Print[n];AppendTo[s,n]],{n,3,1000,3}];s
Select[Range[1000],Mean[IntegerDigits[#^2]]==3&] (* Harvey P. Dale, Jan 13 2015 *)