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A373551 a(n) is the least start of a run of exactly n successive squarefree numbers (A005117) that are odd, or -1 if no such run exists.

%I A373551 #10 Jun 14 2024 11:54:16
%S A373551 1,3,95,15,47,483,5045,6347,266447,1085919,144939,54133739,3348547,
%T A373551 1156672145,952689827,3639059747,49394809937,5496502370531,
%U A373551 8029157726715
%N A373551 a(n) is the least start of a run of exactly n successive squarefree numbers (A005117) that are odd, or -1 if no such run exists.
%e A373551 a(1) = 1, since 1 is the least squarefree number, it is odd, and it is followed by an even squarefree number, 2.
%e A373551 a(2) = 3, since 3 and 5 are two successive squarefree numbers that are odd, preceded by an even squarefree number, 2, and followed by an even squarefree number, 6.
%e A373551 The first 7 terms and the corresponding sets of successive squarefree numbers are:
%e A373551   n |  a(n)  | The n successive squarefree numbers
%e A373551   --|--------|-----------------------------------------
%e A373551   1 |     1  | 1
%e A373551   2 |     3  | 3, 5
%e A373551   3 |    95  | 95, 97, 101
%e A373551   4 |    15  | 15, 17, 19, 21
%e A373551   5 |    47  | 47, 51, 53, 55, 57
%e A373551   6 |   483  | 483, 485, 487, 489, 491, 493
%e A373551   7 |  5045  | 5045, 5051, 5053, 5055, 5057, 5059, 5061
%t A373551 seq[lim_] := Module[{sqf = Select[Range[lim], SquareFreeQ], s = {}, rem, ind}, rem = Join[{0}, Mod[sqf, 2]]; Do[ind = SequencePosition[rem, Join[{0}, Table[1, {k}], {0}], 1]; If[ind == {}, Break[]]; AppendTo[s, sqf[[ind[[1, 1]]]]], {k, 1, Infinity}]; s]; seq[10^7]
%o A373551 (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;}
%Y A373551 Cf. A005117, A039956, A056911, A363192, A373550, A373552.
%K A373551 nonn,hard,more
%O A373551 1,2
%A A373551 _Amiram Eldar_, Jun 09 2024
%E A373551 a(17)-a(19) from _Bert Dobbelaere_, Jun 14 2024