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

1,2

Links

Table of n, a(n) for n=1..49.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A055565, A018072, A018074.

Cf. A348300, A373727.

Sequence in context: A026283 A307287 A373781 * A026045 A371728 A304259

Adjacent sequences: A373911 A373912 A373913 * A373915 A373916 A373917

Keyword

nonn,base,more

Author

Zhining Yang, Jun 22 2024

Status

approved