%I #14 Feb 10 2021 05:35:08

%S 1,2,5,11,11,17,17,37,46,46,112,112,123,149,149,149,257,257,257,257,

%T 257,257,257,261,658,658,685,741,741,1359,1359,1359,1359,1359,1359,

%U 1359,1359,1359,1359,1359,1359,1359,1359,1359,1359,4097,4097,4097,4097,4097

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

%e a(8)=37, values of phi(k) for k=37,..,44 are {36, 18, 24, 16, 40, 12, 42, 20}.

%t 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 (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 Cf. A048892, A079007, A079009.

%K nonn

%O 1,2

%A _Labos Elemer_, Jan 08 2003