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%I #20 May 08 2024 03:44:24
%S 33,85,93,141,201,213,217,301,393,445,633,697,869,921,1041,1137,1189,
%T 1253,1261,1345,1401,1589,1641,1761,1793,1837,1893,1937,1941,1981,
%U 2045,2101,2181,2189,2217,2305,2361,2433,2461,2469,2489,2517,2561,2641,2721
%N Numbers k such that mu(k) + mu(k+1) + mu(k+2) = 3.
%D I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 4th ed., Wiley, NY, 1980, p. 113.
%H Charles R Greathouse IV, <a href="/A063838/b063838.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%t Transpose[ Select[ Partition[ Range[ 3000 ], 3, 1 ], MoebiusMu[ #[ [ 1 ] ] ]+MoebiusMu[ #[ [ 2 ] ] ]+MoebiusMu[ #[ [ 3 ] ] ]==3& ] ][ [ 1 ] ]
%t Position[Partition[MoebiusMu[Range[3000]],3,1],_?(Total[#]==3&)]//Flatten (* _Harvey P. Dale_, May 08 2024 *)
%o (PARI) M(n) = moebius(n)+moebius(n+1)+moebius(n+2); j=[]; for(n=1,5000, if(M(n)==3,j=concat(j,n))); j
%o (PARI) M(n) = moebius(n) + moebius(n + 1) + moebius(n + 2)
%o n=0; for (m=1, 10^9, if(M(m)==3, write("b063838.txt", n++, " ", m); if (n==1000, break))) \\ _Harry J. Smith_, Sep 01 2009
%o (PARI) list(lim)=my(v=List(),run,last); forsquarefree(k=33,lim\1+2, if(moebius(k)==1, if(k[1]-last==1, if(run++>2, listput(v, k[1]-2)), run=1); last=k[1], last=run=0)); Vec(v) \\ _Charles R Greathouse IV_, Jan 08 2018
%Y Cf. A008683. A proper subset of A007675.
%K easy,nonn
%O 1,1
%A _Jason Earls_, Aug 21 2001
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