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.

1, 25, 2187, 703125, 93096125, 10229709861, 197584409639, 32044275110699, 164029657560618375

Offset: 1

Author

Amiram Eldar, May 21 2023

Keywords

• nonn
• more

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

Examples

			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.
		

Crossrefs

Cf. A001694, A062739, A349062, A363189, A363190, A363191.

Programs

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]