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 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. 1
 4, 4, 16, 16, 16, 7972, 7972, 134242, 59716233, 1844284813, 77298251764 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Table of n, a(n) for n=3..13. 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 Cf. A007953. Sequence in context: A369891 A125757 A196065 * A264039 A196064 A220761 Adjacent sequences: A258719 A258720 A258721 * A258723 A258724 A258725 KEYWORD nonn,base,more AUTHOR Giovanni Resta, Jun 08 2015 STATUS approved

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Last modified September 12 20:35 EDT 2024. Contains 375854 sequences. (Running on oeis4.)