This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A258722 #6 Jun 08 2015 06:22:10
%S A258722 4,4,16,16,16,7972,7972,134242,59716233,1844284813,77298251764
%N A258722 a(n) is the smallest k (powers of 10 excluded) such that sod(k), sod(k^2),..., sod(k^n) is an arithmetic progression, where sod(m) = A007953(m) is the sum of the digits of m.
%C A258722 Offset is 3 because an AP of one or two elements makes little sense. Powers of 10 are excluded because they form trivial infinite progressions.
%C A258722 a(14), if it exists, is greater than 4*10^12.
%e A258722 a(5) = 16 because sod(16), sod(16^2),..., sod(16^5) are equal to 7, 13, 19, 25, 31, which is an AP with common difference 6 and 16 is the smallest number with this property.
%t A258722 sod[n_] := Plus @@ IntegerDigits@n; a[n_] := If[n >= 3, Block[{k = 2},
%t A258722 While[ Mod[k, 10] == 0 || 1 < Length@ Union@ Differences[ sod /@ (k^ Range[n])], k++]; k]]; a /@ Range[3, 10]
%Y A258722 Cf. A007953.
%K A258722 nonn,base,more
%O A258722 3,1
%A A258722 _Giovanni Resta_, Jun 08 2015