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
Examples
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.
Links
- Zhining Yang, Table of n, a(n) for n = 1..55
Programs
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C
/* See A373994. */
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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}]