A371728 -id:A371728 - cp's OEIS frontend

A379298 Largest number k for which k^2 is n digits long and has the maximum sum of digits possible for such a square (A371728(n)).

3, 7, 28, 83, 313, 937, 3114, 9417, 29614, 94863, 298327, 987917, 3162083, 9893887, 29983327, 99483667, 315432874, 994927133, 2999833327, 9486778167, 31464263856, 99497231067, 299998333327, 999949483667, 3160522105583, 9892825177313, 29999983333327

Offset: 1

Zhining Yang, Feb 05 2025

			a(6) = 937 because among all 6-digit squares, 698896 = 836^2, 779689 = 883^2, 877969 = 937^2 have the maximum sum of digits 46 = A371728(6), and 937 is the largest.

Cf. A371728, A348303.

Other powers: A380052, A380797, A380566, A380193.

a[n_] := Module[{s = Floor[Sqrt[(10^n - 1)]], max = 0},
   For[k = s, k >= Ceiling[Sqrt[10^(n - 1)]], k--, t = DigitSum[k^2];
    If[t > max, s = k; max = t]]; s];
Table[a[n], {n, 30}]

Conjecture: a(2*n) = A348303(n).

A373914 a(n) is the largest digit sum of all n-digit fourth powers.

Original entry on oeis.org

1, 9, 13, 19, 25, 37, 43, 52, 55, 70, 76, 79, 85, 99, 103, 108, 118, 127, 135, 142, 144, 153, 171, 166, 178, 181, 189, 198, 205, 211, 220, 232, 234, 243, 252, 261, 265, 274, 279, 283, 297, 298, 313, 316, 325, 334, 337, 346, 358

Offset: 1

Zhining Yang, Jun 22 2024

			a(3) = 13 because 13 is the largest digital sum encountered among all 3-digit fourth powers (attained at both fourth powers: 256, 625).

Kevin Ryde, C Code

Cf. A055565, A018072, A018074, A380111, A380797.

Other powers: A371728, A373727, A374025, A373994.

C
```
/* See links. */
```

Table[Max@Map[Total@IntegerDigits[#^4] &, Range[Ceiling[10^((n - 1)/4)], Floor[(10^n-1)^(1/4)]]], {n, 32}]

a(n) = my(m=ceil(10^((n-1)/4)), M=sqrtint(sqrtint(10^n))); vecmax(apply(sumdigits, vector(M-m+1, i, (i+m-1)^4))); \\ Michel Marcus, Jun 23 2024

from sympy import integer_nthroot
def A373914(n): return max(sum(int(d) for d in str(m**4)) for m in range((lambda x:x[0]+(x[1]^1))(integer_nthroot(10**(n-1),4)),1+integer_nthroot(10**n-1,4)[0])) # Chai Wah Wu, Jun 26 2024

A348300 a(n) is the largest number that is the digit sum of the square of an n-digit number.

Original entry on oeis.org

13, 31, 46, 63, 81, 97, 112, 130, 148, 162, 180, 193, 211, 229, 244, 262, 277, 297, 310, 331, 343, 360, 378, 396

Offset: 1

Bernardo Recamán and Freddy Barrera, Oct 10 2021

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

			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.

Cf. A004159, A348303, A370522.

Cf. A371728.

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

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

def A348300(n):
    return max(sum((k^2).digits()) for k in (10^(n-1)..10^n-1))

a(n) = Max_{k=10^(n-1)..10^n-1} A004159(k).

a(11) from Chai Wah Wu, Nov 18 2021
a(12)-a(13) from Martin Ehrenstein, Nov 20 2021
a(14)-a(24) from Zhao Hui Du, Feb 23 2024
Name edited by Jon E. Schoenfield, Mar 10 2024

A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

Original entry on oeis.org

8, 10, 18, 28, 28, 44, 46, 54, 63, 73, 80, 82, 98, 100, 109, 118, 125, 136, 144, 154, 154, 163, 172, 181, 190, 190, 199, 208, 217, 226, 235, 243, 253, 260, 262, 278

Offset: 1

Zhining Yang, Jun 15 2024

			a(7) = 46 because 46 is the largest digital sum encountered among all 7-digit cubes (attained at 3 cubes: 3869893, 7880599, 8998912).

Kevin Ryde, C Code

Cf. A018005, A061439.

Other powers: A371728, A373914, A374025, A373994.

C
```
/* See links. */
```

Table[Max@
  Map[Total@IntegerDigits[#^3] &,
   Range[Ceiling@CubeRoot[10^(n - 1)], CubeRoot[10^n - 1]]], {n, 15}]

from sympy import integer_nthroot
def A373727(n): return max(sum(int(d) for d in str(m**3)) for m in range(1+integer_nthroot(10**(n-1)-1,3)[0],1+integer_nthroot(10**n-1,3)[0])) # Chai Wah Wu, Jun 26 2024

cp's OEIS Frontend

A379298 Largest number k for which k^2 is n digits long and has the maximum sum of digits possible for such a square (A371728(n)).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A373914 a(n) is the largest digit sum of all n-digit fourth powers.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

PARI

Python

A348300 a(n) is the largest number that is the digit sum of the square of an n-digit number.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Python

Sage

Formula

Extensions

A373727 a(n) is the largest number that is the digit sum of an n-digit cube.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

Mathematica

Python