OFFSET
3,1
COMMENTS
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.
a(14), if it exists, is greater than 4*10^12.
EXAMPLE
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.
MATHEMATICA
sod[n_] := Plus @@ IntegerDigits@n; a[n_] := If[n >= 3, Block[{k = 2},
While[ Mod[k, 10] == 0 || 1 < Length@ Union@ Differences[ sod /@ (k^ Range[n])], k++]; k]]; a /@ Range[3, 10]
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Giovanni Resta, Jun 08 2015
STATUS
approved