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A064148
Numbers k such that mu(k) = mu(k+1), where mu is the Möbius function (A008683).
3
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
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Sep 11 2001
STATUS
approved