A363191 a(n) is the least start of a run of exactly n consecutive powerful numbers (A001694) that are even, or -1 if no such run exists.

16, 4, 196, 968, 8712, 437400, 85730400, 5030690600, 264615012500, 5239012864, 550886816376, 2494017320776852

Offset: 1

Author

Amiram Eldar, May 21 2023

Keywords

• nonn
• more

Comments

No more terms below 10^18.

At most one of the n even consecutive powerful numbers in the run is a perfect square. - David A. Corneth, May 21 2023

Examples

			a(1) = 16, since 16 = 2^4 is an even powerful number, preceded by an odd powerful number, 9 = 3^2, and followed by an odd powerful number, 25 = 5^2.
a(2) = 4, since 4 = 2^2 and 8 = 2^3 are two consecutive even powerful numbers, preceded by an odd powerful number, 1, and followed by an odd powerful number, 9 = 3^2.
		

Crossrefs

Cf. A001694, A062739, A349062, A363189, A363190, A363192.

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 = Mod[pow, 2]; Do[ind = SequencePosition[rem, Join[{1}, Table[0, {k}], {1}], 1]; If[ind == {}, Break[]]; AppendTo[s, pow[[ind[[1, 1]] + 1]]], {k, 1, Infinity}]; s]; seq[10^10]