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%I A348300 #77 Jun 26 2024 15:58:43
%S A348300 13,31,46,63,81,97,112,130,148,162,180,193,211,229,244,262,277,297,
%T A348300 310,331,343,360,378,396
%N A348300 a(n) is the largest number that is the digit sum of the square of an n-digit number.
%C A348300 18*n-a(n) appears to be nondecreasing. - _Chai Wah Wu_, Nov 18 2021
%C A348300 According to new data 18*n-a(n) sometimes decreases. - _David A. Corneth_, Feb 21 2024
%C A348300 a(n) is the digit sum of the square of the last n-digit integer in A067179. - _Zhao Hui Du_, Mar 04 2024
%C A348300 a(n) appears to be approximately equal to 16.5*n. - _Zhining Yang_, Mar 12 2024
%C A348300 a(n) modulo 9 is either 0, 1, 4 or 7. - _Chai Wah Wu_, Apr 04 2024
%F A348300 a(n) = Max_{k=10^(n-1)..10^n-1} A004159(k).
%e A348300 a(3) = 46 because 46 is the largest digital sum encountered among the squares (that of 937) of all 3-digit numbers. Such maximal digital sum can be achieved by more than one square (squares of 836 and 883 also have digital sum 46). Largest of these is A348303.
%t A348300 Array[Max@ Map[Total@ IntegerDigits[#^2] &, Range[10^(# - 1), 10^# - 1]] &, 8] (* _Michael De Vlieger_, Oct 12 2021 *)
%o A348300 (Sage)
%o A348300 def A348300(n):
%o A348300     return max(sum((k^2).digits()) for k in (10^(n-1)..10^n-1))
%o A348300 (Python)
%o A348300 def A348300(n): return max(sum(int(d) for d in str(m**2)) for m in range(10**(n-1),10**n)) # _Chai Wah Wu_, Jun 26 2024
%Y A348300 Cf. A004159, A348303, A370522.
%K A348300 nonn,base,more
%O A348300 1,1
%A A348300 _Bernardo Recamán_ and _Freddy Barrera_, Oct 10 2021
%E A348300 a(11) from _Chai Wah Wu_, Nov 18 2021
%E A348300 a(12)-a(13) from _Martin Ehrenstein_, Nov 20 2021
%E A348300 a(14)-a(24) from _Zhao Hui Du_, Feb 23 2024
%E A348300 Name edited by _Jon E. Schoenfield_, Mar 10 2024

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