A356415 a(n) is the least start of exactly n consecutive numbers that have an equal number of even and odd exponents in their prime factorization (A187039), or -1 if no such run of consecutive numbers exists.

1, 44, 603, 906596, 792007675

Offset

1,2

Comments

a(6) > 6.5*10^10, if it exist.

Links

Table of n, a(n) for n=1..5.

Example

a(2) = 44 since 44 = 2^2 * 11 and 45 = 3^2 * 5 both have one even and one odd exponent in their prime factorization, 43 and 46 have no even exponent, and 44 is the least number with this property.

Mathematica

f[p_, e_] := (-1)^e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; seq[len_, nmax_] := Module[{s = Table[0, {len}], v = {1}, n = 2, c = 0, m}, While[c <= len && n <= nmax, If[q[n], v = Join[v, {n}], m = Length[v]; v = {}; If[0 <= m <= len && s[[m]] == 0, c++; s[[m]] = n - m]]; n++]; s]; seq[4, 10^6]

Crossrefs

Cf. A187039, A348076, A348077, A348078.

Sequence in context: A202075 A297680 A264680 * A289647 A252869 A296649

Adjacent sequences: A356412 A356413 A356414 * A356416 A356417 A356418

Keyword

nonn,more

Author

Amiram Eldar, Aug 06 2022

Status

approved