A355434 a(n) is the least start of exactly n consecutive numbers k that are sqrt(k)-smooth (A048098), or -1 if no such run exists.
1, 8, 48, 1518, 5828, 28032, 304260, 290783, 1255500, 4325170, 11135837, 18567909, 321903029, 1394350275, 287946949, 1659945758, 38882519234
Offset: 1
Examples
a(2) = 8 since 8 and 9 are in A048098, 7 and 10 are not, and 8 is the least number with this property.
Programs
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Mathematica
smQ[n_] := FactorInteger[n][[-1, 1]]^2 <= n; seq[len_, nmax_] := Module[{s = Table[0, {len}], v = {1}, n = 2, c = 0, m}, While[c <= len && n <= nmax, If[smQ[n], v = Join[v, {n}], m = Length[v]; v = {}; If[0 <= m <= len && s[[m]] == 0, c++; s[[m]] = n - m]]; n++]; s]; seq[6, 10^5]