cp's OEIS Frontend

A114180 Numbers n with mu(n) = mu(n+1) = mu(n+2).

%I A114180 #9 Jul 23 2023 17:29:34
%S A114180 29,33,41,48,85,93,98,101,124,137,141,201,213,217,229,242,243,281,301,
%T A114180 342,350,393,423,429,433,445,475,548,603,617,633,641,645,697,724,741,
%U A114180 774,821,844,845,846,869,921,969,1021,1024,1041,1085,1129,1137,1189
%N A114180 Numbers n with mu(n) = mu(n+1) = mu(n+2).
%C A114180 Any sequence of 4 or more consecutive numbers with the same value for mu must all have mu(n)=0 (n divisible by a proper square) since at least one of every 4 consecutive numbers is divisible by 4.
%C A114180 A261890(a(n)) = 0. - _Reinhard Zumkeller_, Sep 05 2015
%H A114180 Reinhard Zumkeller, <a href="/A114180/b114180.txt">Table of n, a(n) for n = 1..10000</a>
%e A114180 mu(n)=1 for 33,34,35; 85,86,87; 93,94,95; ...
%e A114180 mu(n)=-1 for 29,30,31; 41,42,43; 101,102,103; ...
%e A114180 mu(n)=0 for 48,49,50; 98,99,100; 124,125,126; ...
%t A114180 SequencePosition[MoebiusMu[Range[1200]],{x_,x_,x_}][[;;,1]] (* _Harvey P. Dale_, Jul 23 2023 *)
%o A114180 (Haskell)
%o A114180 a114180 n = a114180_list !! (n-1)
%o A114180 a114180_list = filter ((== 0) . a261890) [1..]
%o A114180 -- _Reinhard Zumkeller_, Sep 05 2015
%Y A114180 Union of A070258, A063838 and A070268. Cf. A008683, A070284.
%Y A114180  Cf. A261890.
%K A114180 nonn
%O A114180 1,1
%A A114180 _Franklin T. Adams-Watters_, Feb 03 2006