Search: id:A131883
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%I A131883
%S A131883 1,2,2,2,2,4,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,12,12,12,12,
%T A131883 12,12,12,12,12,12,12,12,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
%U A131883 16,16,16,20,20,20,20,20,20,24,24,24,24,24,24,24,24,24,24,24,24,24,24
%N A131883 a(n) = the minimum value from among (phi(n+1),phi(n+2),phi(n+3),...,phi(2n)), 
               where phi(m) (A000010) is the number of positive integers which are 
               coprime to m and are <= m.
%C A131883 Conjecture: After omitting multiple occurrences we get A036912. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Oct 31 2007. This conjecture has been 
               established by Max Alekseyev - see link below.
%C A131883 The Alekseyev link establishes the following explicit relationship between 
               A131883, A036912 and A057635. Namely, for t belonging to A036912, 
               we have t=A131883(A057635(t)-1). In other words, A036912(n) = A131883(A057635(A036912(n))-1) 
               for all n.
%H A131883 M. F. Hasler, <a href="b131883.txt">Table of n, a(n) for n = 1..1000</
               a>
%H A131883 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%H A131883 Max Alekseyev, <a href="a131883.txt">Proof of Jovovic's conjecture</a>
%e A131883 For n = 6 we have phi(7)=6, phi(8)=4, phi(9)=6, phi(10)=4, phi(11)=10, 
               phi(12)=4. The least of these values is 4. So a(6) = 4.
%p A131883 A131883 := proc(n) min(seq(numtheory[phi](i),i=n+1..2*n)) ; end: seq(A131883(n),
               n=1..500) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 
               2007
%t A131883 Table[Min[Table[EulerPhi[i], {i, n + 1, 2*n}]], {n, 1, 80}] - Stefan 
               Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 30 2007
%o A131883 (PARI/gp program from M. F. Hasler, maximilian.hasler(AT)gmail.com, Nov 
               04 2007)
%o A131883 A131883(n)=vecsort(vector(n,i,eulerphi(n+i)))[1]
%o A131883 vector(300,i,A131883(i))
%Y A131883 Sequence in context: A080217 A157901 A072376 this_sequence A113452 A122461 
               A092533
%Y A131883 Adjacent sequences: A131880 A131881 A131882 this_sequence A131884 A131885 
               A131886
%K A131883 nonn
%O A131883 1,2
%A A131883 Leroy Quet Oct 24 2007
%E A131883 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) 
               and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2007

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