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%I #31 Apr 13 2023 10:23:07
%S 3,94863,987917,3162083,29983327,99477133,99483667,994927133,
%T 2428989417,2754991833,2983284917,2999833327,3157196367,9380293167,
%U 9486778167,28105157886,31144643167,31304790167,31459487917,31464263856,94286790167,99497231067,244272388937
%N Numbers whose squares have a digit average greater than 8.
%C There are just 13 terms < 32*10^8.
%C 3 is the only term whose square has a digit average that is an integer.
%C The squares of the first few terms have digit averages 9, 8.1, 8.08333, 8.15385, 8.06667, 8.125, 8.125, 8.22222, 8.05263, 8.05263, 8.10526, 8.10526, 8.05263, ...
%C The sequence contains all numbers of the form floor(30*100^k - 10^k*5/3), k > 5. As of today, we know of only 9 numbers whose square has a digit mean above 8.25: 3, 707106074079263583, 943345110232670883, 94180040294109027313, 2976388751488907738914, 312713447088224669275583, 893241282627485818275387, 314610537013606681884298837387 and 9984988582817657883693383344833. - _M. F. Hasler_, Apr 11 and Apr 13 2023
%H Ed Pegg, <a href="https://mailman.xmission.com/hyperkitty/list/math-fun@mailman.xmission.com/thread/NPPRPLR7JUPAEVAXYAGEKWM4LEJAEYBN/">314610537013606681884298837387</a>, math-fun mailing list, April 11, 2023.
%o (PARI) for(L=1,oo, for(n=sqrtint(10^(L-1)-1)+1,sqrtint(10^L-1), sumdigits(n^2) > 8*L && print1(n", "))) \\ _M. F. Hasler_, Apr 11 2023
%Y Cf. A164771 (s=1), A164770 (s=2), A164782 (s=3), A164776 (s=4), A164774 (s=5), A164779 (s=6), A164773 (s=7), A164772 (s=8).
%Y Cf. A164842 (s < 1).
%K base,nonn
%O 1,1
%A _Zak Seidov_, Aug 28 2009
%E a(14)-a(23) from _Lars Blomberg_, Apr 29 2013
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