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A348300
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a(n) is the largest number that is the digit sum of the square of an n-digit number.
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7
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13, 31, 46, 63, 81, 97, 112, 130, 148, 162, 180, 193, 211, 229, 244, 262, 277, 297, 310, 331, 343, 360, 378, 396
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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18*n-a(n) appears to be nondecreasing. - Chai Wah Wu, Nov 18 2021
According to new data 18*n-a(n) sometimes decreases. - David A. Corneth, Feb 21 2024
a(n) is the digit sum of the square of the last n-digit integer in A067179. - Zhao Hui Du, Mar 04 2024
a(n) appears to be approximately equal to 16.5*n. - Zhining Yang, Mar 12 2024
a(n) modulo 9 is either 0, 1, 4 or 7. - Chai Wah Wu, Apr 04 2024
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LINKS
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FORMULA
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a(n) = Max_{k=10^(n-1)..10^n-1} A004159(k).
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EXAMPLE
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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.
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MATHEMATICA
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Array[Max@ Map[Total@ IntegerDigits[#^2] &, Range[10^(# - 1), 10^# - 1]] &, 8] (* Michael De Vlieger, Oct 12 2021 *)
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PROG
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(Sage)
return max(sum((k^2).digits()) for k in (10^(n-1)..10^n-1))
(Python)
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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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