A380567 a(n) = k the least number for which k^6 is n digits long and the sum of digits of k^6 is the maximum possible for a 6th power of that length (A373994(n)).

1, 2, 3, 4, 6, 7, 12, 16, 23, 46, 64, 96, 143, 202, 277, 461, 547, 977, 1194, 2136, 2896, 3707, 5762, 9763, 13817, 16474, 25847, 43693, 51967, 72539, 121624, 172988, 271427, 463976, 681017, 751204, 1387617, 1732027, 3018897, 3515477, 6765526, 9258023

Offset

1,2

Links

Zhining Yang, Table of n, a(n) for n = 1..55

Example

a(11) = 64 because among all 11-digit sixth powers (47^6-68^6), 64^6=68719476736 and 68^6=98867482624 have the maximum sum of digits, 96 = A373994(11) and 64 is the least number.

Mathematica

a[n_]:=Module[{s=Ceiling[10^((n-1)/6)], max=0}, For[k=s, k<=Floor[(10^n-1)^(1/6)], k++, t=Total@IntegerDigits[k^6]; If[t>max, s=k; max=t]]; s]; Table[a[n], {n, 36}]

Crossrefs

Cf. A370522, A373994, A379650, A379869, A380111, A380193.

Sequence in context: A287924 A039947 A339591 * A380193 A096477 A039059

Adjacent sequences: A380564 A380565 A380566 * A380568 A380569 A380570

Keyword

nonn,base,new

Author

Zhining Yang, Jan 26 2025

Status

approved