cp's OEIS Frontend

A360803 Numbers whose squares have a digit average of 8 or more.

%I A360803 #31 Apr 23 2023 22:47:38
%S A360803 3,313,94863,298327,987917,3162083,9893887,29983327,99477133,99483667,
%T A360803 197483417,282753937,314623583,315432874,706399164,773303937,
%U A360803 894303633,947047833,948675387,989938887,994927133,994987437,998398167,2428989417,2754991833,2983284917,2999833327
%N A360803 Numbers whose squares have a digit average of 8 or more.
%C A360803 This sequence is infinite. For example, numbers floor(30*100^k - (5/3)*10^k) beginning with 2 followed by k 9s, followed by 8 and k 3s, have a square whose digit average converges to (but never equals) 8.25. [Corrected and formula added by _M. F. Hasler_, Apr 11 2023]
%C A360803 Only a few examples are known whose square has a digit average of 8.25 and above: 3^2 = 9, 707106074079263583^2 = 499998999999788997978888999589997889 (digit average 8.25), 94180040294109027313^2 = 8869879989799999999898984986998979999969 (digit average 8.275).
%C A360803 This is the union of A164772 (digit average = 8) and A164841 (digit average > 8). - _M. F. Hasler_, Apr 11 2023
%H A360803 Michael S. Branicky, <a href="/A360822/a360822.py.txt">Python program for OEIS A360822 and searching for squares with < given number of digits < 8</a>
%H A360803 Matthieu Dufour and Silvia Heubach, <a href="https://www.calstatela.edu/sites/default/files/users/u1231/Papers/squares_with_large_ad-preprint.pdf">Squares with Large Digit Average</a>, 2020.
%H A360803 Dmitry Kamenetsky, <a href="/A360803/a360803.txt">The first 68 terms and their digit average</a>
%e A360803 94863 is in the sequence, because 94863^2 = 8998988769, which has a digit average of 8.1 >= 8.
%o A360803 (PARI) isok(k) = my(d=digits(k^2)); vecsum(d)/#d >= 8; \\ _Michel Marcus_, Feb 22 2023
%o A360803 (Python)
%o A360803 def ok(n): d = list(map(int, str(n**2))); return sum(d) >= 8*len(d)
%o A360803 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Feb 22 2023
%Y A360803 Cf. A004159, A185679.
%Y A360803 Cf. A164772 (digit average = 8), A164841 (digit average > 8).
%K A360803 nonn,base
%O A360803 1,1
%A A360803 _Dmitry Kamenetsky_, Feb 21 2023