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

Author

Zhining Yang, Jun 22 2024

Keywords

• nonn
• base
• more

Examples

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

Links

• Kevin Ryde, C Code

Crossrefs

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

Other powers: A371728, A373727, A374025, A373994.

Programs

C

/* See links. */

Mathematica

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

PARI

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

Python

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