cp's OEIS Frontend

A375709 Numbers k such that A013929(k+1) = A013929(k) + 1. In other words, the k-th nonsquarefree number is 1 less than the next nonsquarefree number.

%I A375709 #13 Sep 10 2024 08:04:30
%S A375709 2,8,10,15,17,18,24,28,30,37,38,43,45,47,48,52,56,59,65,67,69,73,80,
%T A375709 85,92,93,94,100,106,108,111,115,122,125,128,133,134,137,138,141,143,
%U A375709 145,148,153,158,165,166,171,178,183,184,192,196,198,203,205,207,210
%N A375709 Numbers k such that A013929(k+1) = A013929(k) + 1. In other words, the k-th nonsquarefree number is 1 less than the next nonsquarefree number.
%C A375709 The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:
%C A375709 - A375709 (difference 1) (this)
%C A375709 - A375710 (difference 2)
%C A375709 - A375711 (difference 3)
%C A375709 - A375712 (difference 4)
%F A375709 Complement of A375710 U A375711 U A375712.
%e A375709 The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by one after the 2nd and 8th terms.
%t A375709 Join@@Position[Differences[Select[Range[100],!SquareFreeQ[#]&]],1]
%Y A375709 Positions of 1's in A078147.
%Y A375709 For prime-powers (A246655) we have A375734.
%Y A375709 First differences are A373409.
%Y A375709 For prime numbers we have A375926.
%Y A375709 For squarefree instead of nonsquarefree we have A375927.
%Y A375709 A005117 lists the squarefree numbers, first differences A076259.
%Y A375709 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A375709 A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.
%Y A375709 A375707 counts squarefree numbers between consecutive nonsquarefree numbers.
%Y A375709 Cf. A007674, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A373410, A373573.
%K A375709 nonn
%O A375709 1,1
%A A375709 _Gus Wiseman_, Sep 01 2024