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A079008 a(n) is smallest number k such that the n successive values of phi(k+j) (j=0,..,n-1) are all distinct.

%I A079008 #14 Feb 10 2021 05:35:08
%S A079008 1,2,5,11,11,17,17,37,46,46,112,112,123,149,149,149,257,257,257,257,
%T A079008 257,257,257,261,658,658,685,741,741,1359,1359,1359,1359,1359,1359,
%U A079008 1359,1359,1359,1359,1359,1359,1359,1359,1359,1359,4097,4097,4097,4097,4097
%N A079008 a(n) is smallest number k such that the n successive values of phi(k+j) (j=0,..,n-1) are all distinct.
%e A079008 a(8)=37, values of phi(k) for k=37,..,44 are {36, 18, 24, 16, 40, 12, 42, 20}.
%t A079008 kul[x_] := Length[x]-Length[Union[x]]; frt[x_] := Table[EulerPhi[x+j], {j, 0, h-1}]; Table[fa=1; k=0; Do[s=frt[n]; s1=kul[s]; If[Equal[s1, 0]&&Equal[fa, 1], k=k+1; Print[{h, n, s}]; fa=0], {n, 1, 10000}], {h, 1, 50}]
%o A079008 (PARI) a(n) = if(n==1, 1, my(v=vector(n, i, eulerphi(i))); for(k=n, oo, if(#Set(v)==n, return(k-n)); v[k%n+1]=eulerphi(k))); \\ _Jinyuan Wang_, Feb 10 2021
%Y A079008 Cf. A048892, A079007, A079009.
%K A079008 nonn
%O A079008 1,2
%A A079008 _Labos Elemer_, Jan 08 2003