A018072 -id:A018072 - cp's OEIS frontend

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

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

A210518 Number of primes up to 10^(n/4).

Original entry on oeis.org

0, 0, 2, 3, 4, 7, 11, 16, 25, 40, 65, 102, 168, 275, 446, 739, 1229, 2039, 3401, 5703, 9592, 16144, 27293, 46243, 78498, 133551, 227647, 388683, 664579, 1138288, 1951957, 3351550, 5761455, 9915892, 17082666, 29458442, 50847534, 87842213, 151876932, 262795354

Offset: 0

Vladimir Pletser, Jan 26 2013

			a(1) = 0 because 10^(1/4) = 1.77828... and there are no primes less than that.
a(2) = 2 because sqrt(10) = 3.16228... and there are 2 primes below that.
a(3) = 3 because 10^(3/4) = 5.62341... and there are 3 primes below that.

Amiram Eldar, Table of n, a(n) for n = 0..80 (calculated using Kim Walisch's primecount)
Kim Walisch, Fast C++ prime counting function implementation (primecount).

Cf. A000720, A006880, A018072.

Table[PrimePi[10^(n/4)], {n, 0, 39}] (* Alonso del Arte, Jan 26 2013 *)

a(n) = primepi(10^(n/4)) = A000720(A018072(n)).

A210522 Decimal expansion of 10^(3/4).

Original entry on oeis.org

5, 6, 2, 3, 4, 1, 3, 2, 5, 1, 9, 0, 3, 4, 9, 0, 8, 0, 3, 9, 4, 9, 5, 1, 0, 3, 9, 7, 7, 6, 4, 8, 1, 2, 3, 1, 4, 6, 8, 2, 5, 1, 0, 4, 3, 0, 9, 8, 6, 9, 1, 6, 6, 4, 0, 8, 1, 6, 8, 9, 4, 2, 3, 7, 3, 5, 8, 8, 3, 5, 6, 8, 6, 4, 3, 0, 6, 2, 8, 4, 8, 9, 0, 5, 8, 5, 7, 9, 8, 4, 5, 2, 6, 2, 2, 0, 3, 0

Offset: 1

Alonso del Arte, Jan 27 2013

This number is the geometric mean of sqrt(10) and 10.
Floor(10^((4*n - 1)/4)) = A018072(4*n - 1) can be obtained by multiplying this number by 10^(n - 1) and truncating the decimal places.
Harriot gives this constant to 18 decimal places. - Charles R Greathouse IV, Oct 22 2014

			5.6234132519034908039495103977648...

P. H. Underwood, "Logarithms" Texas Mathematics Teachers' Bulletin, Vol 6 No. 1 (1920), p. 23.

Thomas Harriot, Manuscript 6782, p. 7, c. 1599.

Cf. A010467, A011007.

Mathematica
```
RealDigits[10^(3/4), 10, 105][[1]]
```

10^.75 \\ Charles R Greathouse IV, Oct 22 2014

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

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A210518 Number of primes up to 10^(n/4).

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A210522 Decimal expansion of 10^(3/4).

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