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A172354 n such that the Moebius function take successively, from n, the values -1,0,-1,0,-1,0.

%I A172354 #16 Aug 18 2025 12:12:16
%S A172354 195,1491,1547,1947,2139,2715,2749,2751,2847,2967,3359,3615,3819,4011,
%T A172354 4013,4015,4047,4155,4547,5019,5449,5647,5741,5779,6351,6353,6355,
%U A172354 6447,6547,6563,6565,6567,6947,6959,6961,6963,7347,7503,7545,7683,8007,9339,10091
%N A172354 n such that the Moebius function take successively, from n, the values -1,0,-1,0,-1,0.
%D A172354 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 826.
%D A172354 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 262 and 287.
%H A172354 Charles R Greathouse IV, <a href="/A172354/b172354.txt">Table of n, a(n) for n = 1..10000</a>
%H A172354 Marc Deléglise and Joël Rivat, <a href="http://projecteuclid.org/euclid.em/1047565447">Computing the summation of the Mobius function</a>, Experiment. Math. 5:4 (1996), pp. 291-295.
%H A172354 Ed Pegg Jr., <a href="https://www.mathpuzzle.com/MAA/02-Mobius%20Function/mathgames_11_03_03.html">The Mobius function (and squarefree numbers)</a>
%H A172354 Primefan, <a href="http://primefan.tripod.com/Mertens2500.html"> Mobius and Mertens Values For n=1 to 2500 </a>
%H A172354 G. Villemin's Almanac of Numbers,<a href="http://villemin.gerard.free.fr/TABLES/aaaFArit/MobiusMe.htm"> Nombres de Moebius et de Mertens</a>
%p A172354 with(numtheory): for n from 1 to 15000 do;if mobius(n)= -1 and mobius(n+1) = 0 and mobius(n+2)= -1 and mobius(n+3)= 0 and mobius(n+4)= -1 and mobius(n+5) = 0 then print(n); else fi ; od;
%t A172354 SequencePosition[MoebiusMu[Range[11000]],{-1,0,-1,0,-1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 17 2016 *)
%o A172354 (PARI) is(n)=moebius(n)<0 && !moebius(n+1) && moebius(n+2)<0 && !moebius(n+3) && moebius(n+4)<0 && !moebius(n+5) \\ _Charles R Greathouse IV_, Sep 26 2013
%Y A172354 Moebius (or Möbius) function mu(n): A008683, A007423, A002321, A002996.
%K A172354 nonn
%O A172354 1,1
%A A172354 _Michel Lagneau_, Feb 01 2010
%E A172354 a(4) inserted by _Charles R Greathouse IV_, Sep 26 2013