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

1,1

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A008683, A074820, A065474.

Sequence in context: A046940 A046939 A082930 * A246299 A161464 A211873

Adjacent sequences: A064145 A064146 A064147 * A064149 A064150 A064151

Keyword

easy,nonn

Author

Jason Earls, Sep 11 2001

Status

approved