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Least k such that the 2^n successive values of phi(k+j) (j=0..2^n-1) are all distinct.
1

%I #21 Aug 27 2024 09:15:30

%S 1,2,11,37,149,1359,14130,175327,1218073,108387730,14305141265

%N Least k such that the 2^n successive values of phi(k+j) (j=0..2^n-1) are all distinct.

%F a(n) = A079008(2^n).

%e For n = 7: a(7) = 175327 because phi(175327+j), for j=0..127 are all distinct: {175326, 87648, ..., 175452, 85320}.

%o (PARI) isdist(v) = forstep(i = #v, 1, -1, forstep(j = i - 1, 1, -1, if(v[i] == v[j], return(j)))); 0;

%o a(n) = {my(m = 2^n, phis = vector(m, i, eulerphi(i)), k = m, ind = isdist(phis)); while(ind != 0, phis = concat(vecextract(phis, Str("^1.."ind)), vector(ind, i, eulerphi(k+i))); k += ind; ind = isdist(phis)); k - m + 1;} \\ _Amiram Eldar_, Aug 27 2024

%Y Cf. A000010, A079008, A079007, A048892.

%K nonn,more

%O 0,2

%A _Labos Elemer_, Jan 10 2003

%E a(8)-a(9) from _Donovan Johnson_, Oct 27 2008

%E a(10) from _Donovan Johnson_, Nov 13 2010