cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A375711 Numbers k such that A013929(k+1) - A013929(k) = 3. In other words, the k-th nonsquarefree number is 3 less than the next nonsquarefree number.

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%I A375711 #6 Sep 10 2024 08:04:38
%S A375711 3,16,23,27,31,44,46,51,55,60,68,74,79,86,95,101,105,107,112,116,121,
%T A375711 126,129,146,147,152,159,164,167,172,177,182,185,191,195,199,204,209,
%U A375711 220,223,229,234,237,242,244,257,262,270,275,285,286,291,299,305,312
%N A375711 Numbers k such that A013929(k+1) - A013929(k) = 3. In other words, the k-th nonsquarefree number is 3 less than the next nonsquarefree number.
%C A375711 The difference of consecutive nonsquarefree numbers is at least 1 and at most 4, so there are four disjoint sequences of this type:
%C A375711 - A375709 (difference 1)
%C A375711 - A375710 (difference 2)
%C A375711 - A375711 (difference 3)
%C A375711 - A375712 (difference 4)
%F A375711 Complement of A375709 U A375710 U A375712.
%e A375711 The initial nonsquarefree numbers are 4, 8, 9, 12, 16, 18, 20, 24, 25, which first increase by 3 after the third term.
%t A375711 Join@@Position[Differences[Select[Range[1000],!SquareFreeQ[#]&]],3]
%Y A375711 Positions of 3's in A078147.
%Y A375711 A005117 lists the squarefree numbers, first differences A076259.
%Y A375711 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A375711 A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.
%Y A375711 A375707 counts squarefree numbers between consecutive nonsquarefree numbers.
%Y A375711 Cf. A007674, A014689, A049094, A061399, A068781, A072284, A110969, A120992, A294242, A373409, A375927.
%K A375711 nonn
%O A375711 1,1
%A A375711 _Gus Wiseman_, Sep 09 2024