A348300 -id:A348300 - cp's OEIS frontend

A348303 a(n) is the largest n-digit number whose square has a digital sum equal to A348300(n).

7, 83, 937, 9417, 94863, 987917, 9893887, 99483667, 994927133, 9486778167, 99497231067, 999949483667, 9892825177313

Offset: 1

Bernardo Recamán and Freddy Barrera, Oct 10 2021

Array[#1 + Position[#2, Max[#2]][[-1, -1]] - 1 & @@ {#1, Map[Total@ IntegerDigits[#^2] &, Range[#1, #2]]} & @@ {10^(# - 1), 10^# - 1} &, 8] (* Michael De Vlieger, Oct 12 2021 *)

a(11) from Chai Wah Wu, Nov 18 2021

a(12)-a(13) from Martin Ehrenstein, Nov 20 2021

A370522 a(n) is the least n-digit number whose square has the maximum sum of digits (A348300(n)).

Original entry on oeis.org

7, 83, 836, 8937, 94863, 987917, 9893887, 99477133, 994927133, 9380293167, 99497231067, 926174913167, 9892825177313, 89324067192437, 943291047332683, 9949874270443813, 83066231922477313, 707106074079263583, 9429681807356492126, 94180040294109027313, 888142995231510436417, 8882505274864168010583

Offset: 1

Zhining Yang, Feb 21 2024

a(n) is the last n-digit term in A067179.

As the last two of the only nine known numbers whose square has a digit mean above 8.25 (see A164841), there is a high probability that a(30)=314610537013606681884298837387 and a(31)=9984988582817657883693383344833.

			a(3) = 836 because among all 3-digit numbers, 836 is the smallest whose square 698896 has the maximum sum of digits, 46 = A348300(3).

Zhining Yang, Table of n, a(n) for n = 1..24 (terms 11..24 from Zhao Hui Du)

Cf. A004159, A067179, A348300, A348303.

A348300={13,31,46,63,81,97,112,130,148,162,180};
A370522[n_]:=Do[If[Total@IntegerDigits[k^2]==A348300[[n]],Return[k];],{k,10^(n-1),10^n-1}];
Table[A370522[n],{n,8}]

def A370522(n):
    A348300=[0,13,31,46,63,81,97,112,130,148,162,180]
    for k in range(10**(n-1), 10**n):
        if sum(int(d) for d in str(k**2))==A348300[n]:
            return(k)
print([A370522(n) for n in range(1,9)])

a(11)-a(24) from Zhao Hui Du, Feb 23 2024

A374025 a(n) is the largest digit sum of all n-digit fifth powers.

Original entry on oeis.org

1, 5, 9, 27, 27, 36, 45, 46, 52, 63, 72, 80, 89, 90, 99, 104, 108, 119, 126, 143, 137, 152, 157, 162, 175, 180, 182, 189, 198, 208, 209, 216, 225, 234, 236, 250, 253, 270, 270, 284, 286, 288, 297, 310, 315, 323, 324, 334, 341, 346, 351, 364

Offset: 1

Zhining Yang, Jun 25 2024

			a(5) = 27 because 27 is the largest digital sum encountered among all 5-digit fifth powers (16807, 32768, 59049).

Cf. A055566, A018141, A018143, A348300, A373727, A373914.

Table[Max@Map[Total@IntegerDigits[#^5] &, Range[Ceiling[10^((n - 1)/5)], Floor[(10^n-1)^(1/5)]]], {n, 40}]

from sympy import integer_nthroot
def A374025(n): return max(sum(int(d) for d in str(m**5)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),5)),1+integer_nthroot(10**n-1,5)[0])) # Chai Wah Wu, Jun 26 2024

a(41)-a(49) from Chai Wah Wu, Jun 26 2024

a(50)-a(52) from Chai Wah Wu, Jun 27 2024

A373994 a(n) is the largest digit sum of all n-digit sixth powers.

Original entry on oeis.org

1, 10, 18, 19, 27, 28, 45, 37, 46, 64, 64, 81, 82, 82, 91, 100, 100, 118, 117, 126, 136, 136, 154, 154, 163, 163, 172, 181, 181, 190, 199, 208, 217, 226, 235, 235, 243, 244, 261, 262, 280, 280, 280, 289, 298, 298, 307, 325, 325, 325, 334, 352, 352, 361, 370

Offset: 1

Zhining Yang, Jun 26 2024

			a(6) = 28 because 28 is the largest digital sum encountered among all 6-digit sixth powers (117649, 262144, 531441).

Kevin Ryde, C Code

Cf. A001014, A348300, A373727, A373914, A374025.

C
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/* See links. */
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Table[Max@Map[Total@IntegerDigits[#^6] &, Range[Ceiling[10^((n - 1)/6)], Floor[(10^n-1)^(1/6)]]], {n, 42}]

A371728 a(n) is the largest number that is the digit sum of an n-digit square number.

Original entry on oeis.org

9, 13, 19, 31, 40, 46, 54, 63, 70, 81, 88, 97, 106, 112, 121, 130, 136, 148, 154, 162, 171, 180, 187, 193, 205, 211, 220, 229, 235, 244, 253, 262, 271, 277, 286, 297, 301, 310, 319, 331, 334, 343, 355, 360, 367, 378, 388, 396

Offset: 1

Zhining Yang, Apr 04 2024

a(n) appears to be approximately equal to (33*n-11)/4.

			a(6) = 46 because 46 is the largest digital sum encountered among all 6-digit squares (698896, 779689, 877969).

Shouen Wang, Chinese BBS: How many of these A's are there?

Cf. A004159, A049415, A069665, A069666.

Cf. A056991, A348300, A379298.

Array[Max@Map[Total@IntegerDigits[#^2] &, Range[Floor@Sqrt[10^(#)]], Floor@Sqrt[10^(# + 1) - 1]] &, 15]

a(22)-a(48) from Zhao Hui Du, Apr 05 2024
a(49)-a(62) from Zhining Yang, May 08 2024
a(63)-a(64) from Zhining Yang, May 23 2024
Incorrect a(61) and unverified a(49) onward deleted by Zhining Yang, Mar 03 2025

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A348303 a(n) is the largest n-digit number whose square has a digital sum equal to A348300(n).

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A370522 a(n) is the least n-digit number whose square has the maximum sum of digits (A348300(n)).

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A374025 a(n) is the largest digit sum of all n-digit fifth powers.

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A373994 a(n) is the largest digit sum of all n-digit sixth powers.

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A371728 a(n) is the largest number that is the digit sum of an n-digit square number.

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Programs

Mathematica

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