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 A363192 a(n) is the least start of a run of exactly n consecutive powerful numbers (A001694) that are odd, or -1 if no such run exists. 6
 1, 25, 2187, 703125, 93096125, 10229709861, 197584409639, 32044275110699, 164029657560618375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS No more terms below 10^18. At most one of the n odd consecutive powerful numbers in the run is a perfect square. - David A. Corneth, May 21 2023 LINKS Table of n, a(n) for n=1..9. EXAMPLE a(1) = 1, since 1 is an odd powerful number, followed by an even powerful number, 4 = 2^2. a(2) = 25, since 25 = 5^2 and 27 = 3^3 are two consecutive odd powerful numbers, preceded by an even powerful number, 16 = 2^4, and followed by an even powerful number, 32 = 2^5. MATHEMATICA seq[lim_] := Module[{pow = Union[Flatten[Table[i^2*j^3, {j, 1, lim^(1/3)}, {i, 1, Sqrt[lim/j^3]}]]], s = {}, rem, ind}, rem = Join[{0}, Mod[pow, 2]]; Do[ind = SequencePosition[rem, Join[{0}, Table[1, {k}], {0}], 1]; If[ind == {}, Break[]]; AppendTo[s, pow[[ind[[1, 1]]]]], {k, 1, Infinity}]; s]; seq[1.1*10^10] CROSSREFS Cf. A001694, A062739, A349062, A363189, A363190, A363191. Sequence in context: A197430 A195272 A266130 * A222276 A304323 A135057 Adjacent sequences: A363189 A363190 A363191 * A363193 A363194 A363195 KEYWORD nonn,more AUTHOR Amiram Eldar, May 21 2023 STATUS approved

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Last modified June 22 05:36 EDT 2024. Contains 373565 sequences. (Running on oeis4.)