A373552 a(n) is the least start of a run of exactly n successive squarefree numbers (A005117) that are even, or -1 if no such run exists.
2, 422, 2522, 1674274, 24697404970, 4014578863358
Offset: 1
Examples
a(1) = 2, since 2 is an even squarefree number, preceded by an odd squarefree number, 3, and followed by an odd squarefree number, 3. a(2) = 422, since 422 and 426 are two successive squarefree numbers that are even, preceded by an odd squarefree number, 421, and followed by an odd squarefree number, 427. The first 4 terms and the corresponding sets of successive squarefree numbers are: n | a(n) | The n successive squarefree numbers --|---------------|------------------------------------ 1 | 2 | 1 2 | 422 | 422, 426 3 | 2522 | 2522, 2526, 2530 4 | 1674274 | 1674274, 1674278, 1674282, 1674286
Programs
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Mathematica
seq[lim_] := Module[{sqf = Select[Range[lim], SquareFreeQ], s = {}, rem, ind}, rem = Join[{1}, Mod[sqf, 2]]; Do[ind = SequencePosition[rem, Join[{1}, Table[0, {k}], {1}], 1]; If[ind == {}, Break[]]; AppendTo[s, sqf[[ind[[1, 1]]]]], {k, 1, Infinity}]; s]; seq[2*10^6] -
PARI
lista(len, kmax = oo) = {my(v = vector(len), c = 0, k = 1, k0, i = 0); while(c < len && k < kmax, if(issquarefree(k), if(!(k % 2), i++; if(i == 1, k0 = k), if(i > 0 && i <= len && v[i] == 0, v[i] = k0; c++); i = 0)); k++); v;}
Extensions
a(6) from Bert Dobbelaere, Jun 14 2024