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%I #17 Apr 11 2023 21:02:33
%S 145,152,179,190,251,3182,3190,3199,3245,3290,3335,3362,3380,3470,
%T 3479,3496,3550,3649,3650,3749,3821,4001,4010,4100,4495,4496,4540,
%U 4550,4585,4595,4639,4649,4810,4820,4910,4990,5701,5710,5755,5800,5900,6350,6404
%N Numbers k with the property that the average digit of k^2 is 2.
%C There are 6368 such k's < 10^7: see link to 15217.html.
%H Harvey P. Dale, <a href="/A164770/b164770.txt">Table of n, a(n) for n = 1..2500</a>
%H Zak Seidov, <a href="http://zak08.livejournal.com/15217.html">Average digit of n^2 is 2.</a>
%H Zak Seidov, <a href="http://zak08.livejournal.com/14963.html">Case with trailing zeros.</a>
%e 145 is a term because 145^2 = 21025 and (2 + 1 + 0 + 2 + 5)/5 = 2.
%t Select[Range[6500],Mean[IntegerDigits[#^2]]==2&] (* _Harvey P. Dale_, May 10 2021 *)
%o (PARI) dsum(n)={my(s=0);while(n>9,s+=n%10;n\=10);s+n};
%o for(n=1,1e6,if(dsum(n^2)/#Str(n^2)==2,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
%E Edited by _Charles R Greathouse IV_, Mar 23 2010
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