cp's OEIS Frontend

A375710 Numbers k such that A013929(k+1) - A013929(k) = 2. In other words, the k-th nonsquarefree number is 2 less than the next nonsquarefree number.

%I A375710 #6 Sep 10 2024 08:04:42
%S A375710 5,6,9,19,20,21,33,34,36,49,57,58,62,63,66,76,77,88,89,91,96,97,103,
%T A375710 104,113,114,118,119,130,131,132,136,142,149,150,161,162,174,175,187,
%U A375710 188,189,190,201,202,206,215,217,218,225,226,231,232,245,246,249,253
%N A375710 Numbers k such that A013929(k+1) - A013929(k) = 2. In other words, the k-th nonsquarefree number is 2 less than the next nonsquarefree number.
%C A375710 The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:
%C A375710 - A375709 (difference 1)
%C A375710 - A375710 (difference 2)
%C A375710 - A375711 (difference 3)
%C A375710 - A375712 (difference 4)
%F A375710 Complement of A375709 U A375711 U A375712.
%e A375710 The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by 2 after the fifth and sixth terms.
%t A375710 Join@@Position[Differences[Select[Range[1000], !SquareFreeQ[#]&]],2]
%Y A375710 Positions of 2's in A078147.
%Y A375710 For prime numbers we have A029707.
%Y A375710 For nonprime numbers we appear to have A014689.
%Y A375710 A005117 lists the squarefree numbers, first differences A076259.
%Y A375710 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A375710 A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.
%Y A375710 A375707 counts squarefree numbers between consecutive nonsquarefree numbers.
%Y A375710 Cf. A007674, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A373409, A373573, A375927.
%K A375710 nonn
%O A375710 1,1
%A A375710 _Gus Wiseman_, Sep 09 2024