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.

A071320 Least of four consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2, k+3} are in A067259.

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%I A071320 #30 Jan 18 2023 03:25:03
%S A071320 844,1681,8523,8954,10050,10924,11322,17404,19940,22020,23762,24450,
%T A071320 25772,27547,30923,30924,33172,34347,38724,39050,39347,40050,47673,
%U A071320 47724,47825,49147,54585,55449,57474,58473,58849,58867,59924,62865
%N A071320 Least of four consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2, k+3} are in A067259.
%C A071320 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 0, 1, 4, 57, 555, 5492, 55078, 551443, 5512825, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000551... . - _Amiram Eldar_, Jan 18 2023
%H A071320 Amiram Eldar, <a href="/A071320/b071320.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Michael De Vlieger)
%F A071320 A051903(k) = A051903(k+1) = A051903(k+2) = A051903(k+3) = 2 when k is a term.
%e A071320 k = 844 is a term since 844 = 2^2*211, k+1 = 845 = 5*13^2, k+2 = 846 = 2*3^2*47, and k+4 = 847 = 7*11^2.
%t A071320 With[{s = Select[Range[10^5], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ SequencePosition[t, {1, 1, 1}][[All, 1]]]@ Differences@ s] (* _Michael De Vlieger_, Jul 30 2017 *)
%Y A071320 Subsequence of A067259, A071318 and A071319.
%Y A071320 Cf. A051903, A063528.
%K A071320 nonn
%O A071320 1,1
%A A071320 _Labos Elemer_, May 29 2002