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%I M1874 #53 Mar 05 2019 14:47:28
%S 1,2,8,48,80,96,128,240,288,480,1008,1200,1296,1440,1728,2592,2592,
%T 4800,5600,6480,8640,11040,12480,14976,19008,19200,22464,24320,24576,
%U 21120,28416,27840,25920,32000,32768,36000,47520,52992,60480,59904,79200,89280,96768
%N Values of phi(n) = phi(n+1).
%C In other words, consider n = 1,2,3,4,..., and if phi(n)=phi(n+1), add phi(n) to the sequence.
%D R. K. Guy, Unsolved Problems Number Theory, Sect. B36.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A003275/b003275.txt">Table of n, a(n) for n=1..2567</a>
%H K. Miller, <a href="/A003275/a003275.pdf">The equation phi(n) = phi(n+1)</a>, Unpublished M.S., ND..
%H K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. Unpublished, 1972. [ See <a href="http://dx.doi.org/10.1090/S0025-5718-73-99703-2">Review</a>, Math. Comp., Vol. 27, p. 447-448, 1973 ].
%H K. Miller, <a href="/A003275/a003275_1.pdf">Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000</a>, Mathematics of Computation 27 (1973), 47-48. (Annotated scanned copy)
%H Leo Moser, <a href="http://www.jstor.org/stable/2305815">Some equations involving Euler's totient function</a>, Amer. Math. Monthly, 56 (1949), 22-23.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>
%F a(n) = A000010(A001274(n)). - _Reinhard Zumkeller_, May 20 2014
%t Cases[Split[Table[EulerPhi[k],{k,1,50000}]],{_,_}][[1;;27,1]] (* _Jean-François Alcover_, Mar 20 2011 *)
%t #[[1]]&/@Select[Partition[EulerPhi[Range[80000]],2,1],#[[1]]==#[[2]]&] (* _Harvey P. Dale_, Oct 03 2012 *)
%t SequenceCases[EulerPhi[Range[200000]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 05 2019 *)
%o (Haskell)
%o a003275 = a000010 . fromIntegral . a001274
%o -- _Reinhard Zumkeller_, May 20 2014
%Y Cf. A000010, A001274.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
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