%I A066494
%S A066494 1,3,8,9,12,18,24
%N A066494 Numbers n such that p(n+1)-p(n) = EulerPhi(n), where p(n) denotes the 
               n-th prime.
%C A066494 After 24, there are no more terms < 10^6. Are there any more terms?
%C A066494 This sequence is certainly finite and very likely complete. phi(n) is 
               bounded below asymptotically by n/log log n * e^{-gamma}, while prime 
               gaps are known to be bounded asymptotically above by p^{1/3} ~ (n 
               log n)^(1/3). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 
               27 2006
%e A066494 p(13)-p(12) = 41 - 37 = 4 = EulerPhi(12); so 12 belongs to the sequence.
%t A066494 f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^6], f[ # ] == EulerPhi[ 
               # ] &]
%Y A066494 Sequence in context: A080761 A087286 A165289 this_sequence A082721 A071677 
               A084747
%Y A066494 Adjacent sequences: A066491 A066492 A066493 this_sequence A066495 A066496 
               A066497
%K A066494 more,nonn,fini
%O A066494 1,2
%A A066494 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 03 2002