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%I #6 Oct 30 2013 04:37:02
%S 2,1,2,1,10,2,6,7,4,5,14,3,22,7,2,1,34,3,18,12,14,3,46,8,16,9,10,7,58,
%T 2,30,19,8,17,30,3,36,19,26,11,82,3,86,11,20,23,94,3,80,5,34,13,106,3,
%U 68,9,16,29,118,4,82,15,10,21,32,9,94,17,20,34,142,32,112,17,48,15,66,26
%N Least k such that phi(n+k)=2*phi(n), where phi is Euler's totient function.
%C Makowski shows that a k exists for each n. It appears that k<=2n. For prime n, it appears that n-1<=k<=2n.
%D R. K. Guy, Unsolved Problems in Number Theory, 3rd Ed., New York, Springer-Verlag, 2004, Section B36.
%D Andrzej Makowski, On the equation phi(n+k)=2*phi(n), Elem. Math., 29 (1974), 13.
%H Donovan Johnson, <a href="/A110179/b110179.txt">Table of n, a(n) for n = 1..10000</a>
%t Table[k=1; e=EulerPhi[n]; While[EulerPhi[n+k] != 2e, k++ ]; k, {n, 100}]
%Y Cf. A050473 (least k such that phi(n+k)=2*phi(k)).
%K nonn
%O 1,1
%A _T. D. Noe_, Jul 15 2005
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