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

195, 1491, 1547, 1947, 2139, 2715, 2749, 2751, 2847, 2967, 3359, 3615, 3819, 4011, 4013, 4015, 4047, 4155, 4547, 5019, 5449, 5647, 5741, 5779, 6351, 6353, 6355, 6447, 6547, 6563, 6565, 6567, 6947, 6959, 6961, 6963, 7347, 7503, 7545, 7683, 8007, 9339, 10091

Offset: 1

Author

Michel Lagneau, Feb 01 2010

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 826.
• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 262 and 287.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Marc Deléglise and Joël Rivat, Computing the summation of the Mobius function, Experiment. Math. 5:4 (1996), pp. 291-295.
• Ed Pegg Jr., The Mobius function (and squarefree numbers)
• Primefan, Mobius and Mertens Values For n=1 to 2500
• G. Villemin's Almanac of Numbers, Nombres de Moebius et de Mertens

Crossrefs

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

Programs

Maple

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;

Mathematica

SequencePosition[MoebiusMu[Range[11000]],{-1,0,-1,0,-1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 17 2016 *)

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

Extensions

a(4) inserted by Charles R Greathouse IV, Sep 26 2013