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.
%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