A380566 a(n) = k is the largest k for which k^5 is n digits long and the sum of digits of k^5 is the maximum for any n digit 5th power (A374025).
1, 2, 3, 6, 9, 15, 18, 37, 58, 93, 156, 179, 368, 579, 756, 1379, 2337, 3965, 6006, 9746, 14198, 25046, 38779, 60006, 98746, 151446, 231755, 389658, 585516, 819199, 1584779, 2452779, 3897999, 5400759, 9744998, 15517759, 23936959, 28737498, 62943519, 95635199, 156373159, 225142779, 351816939, 595519999
Offset: 1
Examples
a(14) = 579 because among all 14-digit fifth powers(399^5-630^5), 549^5=49872566977749,579^5=65071799758899, both have the maximum sum of digits, 90 = A374025(14) and 579 is the largest.
Links
- Zhining Yang, Table of n, a(n) for n = 1..52
Programs
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Mathematica
a[n_]:=Module[{m=Floor[(10^n-1)^(1/5)],max=0},For[k=m,k>=Ceiling[10^((n-1)/5)],k--,t=Total@IntegerDigits[k^5];If[t>max,s=k;max=t]];s];Table[a[n],{n,30}]