A172354 - OEIS

%I #14 Sep 17 2016 09:16:22

%S 195,1491,1547,1947,2139,2715,2749,2751,2847,2967,3359,3615,3819,4011,

%T 4013,4015,4047,4155,4547,5019,5449,5647,5741,5779,6351,6353,6355,

%U 6447,6547,6563,6565,6567,6947,6959,6961,6963,7347,7503,7545,7683,8007,9339,10091

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

%D 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 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 Charles R Greathouse IV, <a href="/A172354/b172354.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Ed Pegg Jr., <a href="http://www.maa.org/editorial/mathgames/mathgames_11_03_03.html">The Mobius function (and squarefree numbers)</a>

%H Primefan, <a href="http://primefan.tripod.com/Mertens2500.html"> Mobius and Mertens Values For n=1 to 2500 </a>

%H 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 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 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 (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 Moebius (or Möbius) function mu(n): A008683, A007423, A002321, A002996.

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 01 2010

%E a(4) inserted by _Charles R Greathouse IV_, Sep 26 2013