A063838 Numbers k such that mu(k) + mu(k+1) + mu(k+2) = 3.

33, 85, 93, 141, 201, 213, 217, 301, 393, 445, 633, 697, 869, 921, 1041, 1137, 1189, 1253, 1261, 1345, 1401, 1589, 1641, 1761, 1793, 1837, 1893, 1937, 1941, 1981, 2045, 2101, 2181, 2189, 2217, 2305, 2361, 2433, 2461, 2469, 2489, 2517, 2561, 2641, 2721

Offset: 1

Author

Jason Earls, Aug 21 2001

Keywords

• easy
• nonn

References

• I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 4th ed., Wiley, NY, 1980, p. 113.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A008683. A proper subset of A007675.

Programs

Mathematica

Transpose[ Select[ Partition[ Range[ 3000 ], 3, 1 ], MoebiusMu[ #[ [ 1 ] ] ]+MoebiusMu[ #[ [ 2 ] ] ]+MoebiusMu[ #[ [ 3 ] ] ]==3& ] ][ [ 1 ] ]
Position[Partition[MoebiusMu[Range[3000]],3,1],?(Total[#]==3&)]//Flatten (* _Harvey P. Dale, May 08 2024 *)

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

PARI

M(n) = moebius(n) + moebius(n + 1) + moebius(n + 2)
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

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