cp's OEIS Frontend

A277261 Least k>0 such that phi(Fibonacci(n)) divides phi(Fibonacci(n+k)).

%I A277261 #17 Dec 03 2016 12:32:37
%S A277261 1,1,1,1,1,1,1,4,3,5,11,2,13,5,6,16,17,6,16,10,14,11,23,20,25,13,22,
%T A277261 14,29,10,31,32,22,17,35,36,37,38,26,20,41,42,43,44,18,46,47,48,49,50,
%U A277261 51,26,53,54,55,56,57,58,59,60,61,31,63,64,65,66,67,68,69,70,71,72,73,37,75,76,77,78,79,80,81,41
%N A277261 Least k>0 such that phi(Fibonacci(n)) divides phi(Fibonacci(n+k)).
%C A277261 a(n) <= n, since Fibonacci(n) divides Fibonacci(2n) and phi(x) divides phi(y) if x divides y. - _Robert Israel_, Dec 01 2016
%e A277261 a(7) = 1 because phi(Fibonacci(7)) = phi(Fibonacci(8)) = 12.
%p A277261 f:= proc(n) uses combinat, numtheory; local k, phin;
%p A277261     phin:= phi(fibonacci(n));
%p A277261     for k from 1 do if phi(fibonacci(n+k)) mod phin = 0 then return k fi od
%p A277261 end proc;
%p A277261 map(f, [$1..100]); # _Robert Israel_, Dec 01 2016
%t A277261 Table[k = 1; While[Mod[EulerPhi@ Fibonacci[n + k], EulerPhi@ Fibonacci@ n] != 0, k++]; k, {n, 82}] (* _Michael De Vlieger_, Nov 23 2016 *)
%o A277261 (PARI) a(n) = {my(k=1); while (eulerphi(fibonacci(n+k)) % eulerphi(fibonacci(n)), k++); k;} \\ _Michel Marcus_, Nov 19 2016
%Y A277261 Cf. A000010, A000045, A065449.
%K A277261 nonn
%O A277261 1,8
%A A277261 _Altug Alkan_, Oct 07 2016