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%I #28 Sep 01 2020 08:40:35
%S 2,8,14,21,24,27,29,30,33,34,38,41,42,44,48,49,57,63,66,70,75,78,80,
%T 85,86,93,94,98,99,101,102,109,113,116,118,120,122,124,125,130,133,
%U 135,137,138,141,142,145,147,152,158,168,171,173,175,177,181,188,190,201
%N Numbers k such that mu(k) = mu(k+1), where mu is the Möbius function (A008683).
%H Amiram Eldar, <a href="/A064148/b064148.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)
%F 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
%e 2 is a term since mu(2) = mu(3) = -1.
%t SequencePosition[MoebiusMu[Range[250]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 26 2017 *)
%o (PARI) j=[]; for(n=1,500, if(moebius(n)==moebius(n+1),j=concat(j,n))); j
%o (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
%Y Cf. A008683, A074820, A065474.
%K easy,nonn
%O 1,1
%A _Jason Earls_, Sep 11 2001
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