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 A171262 Numbers n such that phi(n) = 2*phi(n+1). 7
 5, 13, 35, 37, 61, 73, 157, 193, 277, 313, 397, 421, 455, 457, 541, 613, 661, 665, 673, 733, 757, 877, 997, 1085, 1093, 1153, 1201, 1213, 1237, 1295, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2169, 2341, 2473, 2557, 2593, 2797, 2857 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Theorem: A prime p is in the sequence iff 1/2*(p+1) is prime. Proof: If both numbers p & 1/2*(p+1) are prime then phi(p)=p-1=2*(p-1)/2 2*(1/2*(p+1)-1)=2*phi(1/2*(p+1)), 1/2*(p+1) is odd so phi(1/2*(p+1))= phi(p+1) hence phi(p)=2*phi(p+1), namely p is in the sequence. Also if p is a prime term of the sequence then phi(p)=2*phi(p+1) so p-1=2*phi(p+1) or phi(p+1)=1/2*(p+1)-1 hence 1/2*(p+1)is prime. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 FORMULA phi(35)=2*12=2*phi(35+1), so 35 is in the sequence. MATHEMATICA Select[Range[2900], EulerPhi[ # ]==2EulerPhi[ #+1]&] PROG (MAGMA) [n: n in [1..3*10^3] | EulerPhi(n) eq 2*EulerPhi(n+1)]; // Vincenzo Librandi, Apr 14 2015 CROSSREFS Cf. A005383, A171271. Sequence in context: A034521 A294841 A092647 * A006561 A146845 A192310 Adjacent sequences:  A171259 A171260 A171261 * A171263 A171264 A171265 KEYWORD nonn,easy AUTHOR Farideh Firoozbakht, Feb 23 2010 STATUS approved

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Last modified December 7 20:04 EST 2021. Contains 349585 sequences. (Running on oeis4.)