A064148 Numbers k such that mu(k) = mu(k+1), where mu is the Möbius function (A008683).

2, 8, 14, 21, 24, 27, 29, 30, 33, 34, 38, 41, 42, 44, 48, 49, 57, 63, 66, 70, 75, 78, 80, 85, 86, 93, 94, 98, 99, 101, 102, 109, 113, 116, 118, 120, 122, 124, 125, 130, 133, 135, 137, 138, 141, 142, 145, 147, 152, 158, 168, 171, 173, 175, 177, 181, 188, 190, 201

Offset: 1

Author

Jason Earls, Sep 11 2001

Keywords

• easy
• nonn

Examples

			2 is a term since mu(2) = mu(3) = -1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A008683, A074820, A065474.

Programs

Mathematica

SequencePosition[MoebiusMu[Range[250]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 26 2017 *)

PARI

j=[]; for(n=1,500, if(moebius(n)==moebius(n+1),j=concat(j,n))); j

PARI

{ n=0; for (m=1, 10^9, if (moebius(m)==moebius(m + 1), write("b064148.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 09 2009

Formula

a(n) seems to be asymptotic to c*n with c=3.7.... Using heuristic arguments (cf. A074820): c maybe = 1/(3A/2 + 1 - 12/Pi^2) ~ 3.729994018, where A ~ 0.3226340989 is the product over all primes p of 1 - 2/p^2 (cf. A065474). - Benoit Cloitre, Sep 08 2002