A164778 - OEIS

%I #11 Apr 11 2023 21:01:56

%S 24,27,387,417,423,447,528,537,543,624,663,678,684,687,714,768,774,

%T 786,813,816,822,828,834,864,867,876,882,888,891,894,924,927,933,936,

%U 942,948,957,963,969,972,978,984,987,993,10386,11313,11772,12114,12186

%N Numbers n with property that average digit of n^2 is s=6.

%C All terms are multiples of 3.

%H Harvey P. Dale, <a href="/A164778/b164778.txt">Table of n, a(n) for n = 1..1000</a>

%e 24^2 = 576 and (5 + 7 + 6)/3 = 6

%e 387^2 = 149769 and (1 + 4 + 9 + 7 + 6 + 9)/6 = 6.

%t s={};me=6;Do[If[me==Mean[IntegerDigits[n^2]],Print[n];AppendTo[s,n]],{n,3,10^4,3}];s

%t Select[3*Range[5000],Mean[IntegerDigits[#^2]]==6&] (* _Harvey P. Dale_, Aug 17 2014 *)

%o (PARI) dsum(n)={my(s=0);while(n>9,s+=n%10;n\=10);s+n};

%o forstep(n=3,1e6,3,if(dsum(n^2)/#Str(n^2)==6,print1(n","))) \\ _Charles R Greathouse IV_, Nov 01 2009

%Y Subsequence of A164817.

%Y 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 base,nonn

%O 1,1

%A _Zak Seidov_, Aug 26 2009