A379650 a(n) is the least number whose fifth power is an n-digit fifth power which has the maximum sum of digits (A374025(n)).

1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 549, 756, 1379, 2139, 3965, 4956, 9746, 11156, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 1776339, 3803469, 5400759, 9744998, 11463799, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999

Offset: 1

Author

Zhining Yang, Jan 12 2025

Keywords

• nonn
• base

Examples

			a(7) = 18 because among all 7-digit fifth powers (16^5 to 25^5), 18^5=1889568 is the item which has the maximum sum of digits, 45 = A374025(7).
		

Links

• Zhining Yang, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A000584, A374025.

Cf. A370522, A373914, A379869, A380111.

Programs

Mathematica

a[n_]:=Module[{s=Floor[(10^n-1)^(1/5)],max=0},
For[k=s,k>=Ceiling[10^((n-1)/5)],k--,t=DigitSum[k^5];
If[t>max,s=k;max=t]];s];
For[n=1,n<=30,n++,Print[{n,a[n]}]]