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Numbers n such that phi(n) + 1 and phi(n) - 1 are twin primes.
10

%I #23 Sep 29 2019 03:03:44

%S 5,7,8,9,10,12,13,14,18,19,21,26,27,28,31,36,38,42,43,49,54,61,62,73,

%T 77,86,91,93,95,98,99,103,109,111,117,122,124,133,135,139,146,148,151,

%U 152,154,171,181,182,186,189,190,193,198,199,206,209,216,217,218,221,222

%N Numbers n such that phi(n) + 1 and phi(n) - 1 are twin primes.

%C Phi(n) is middle term between twin primes (A014574). Union of A006512 and A068019; intersection of A039698 and A078892. - _Ray Chandler_, May 26 2008

%C The positions of isolated nonprimes in A000010. - _Juri-Stepan Gerasimov_, Nov 10 2009

%H Amiram Eldar, <a href="/A072281/b072281.txt">Table of n, a(n) for n = 1..10000</a>

%e phi(14) + 1 = 7 and phi(14) - 1 = 5, so 14 is a term of the sequence.

%t Select[Range[10^3], PrimeQ[EulerPhi[ # ] + 1] && PrimeQ[EulerPhi[ # ] - 1] &]

%t Select[Range[300],And@@PrimeQ[EulerPhi[#]+{1,-1}]&] (* _Harvey P. Dale_, Apr 07 2012 *)

%o (PARI) isok(n) = my(p); isprime(p=eulerphi(n)-1) && isprime(p+2); \\ _Michel Marcus_, Sep 29 2019

%Y Cf. A000010, A000040, A006512, A014574, A039698, A068019, A078892.

%K easy,nonn

%O 1,1

%A _Joseph L. Pe_, Jul 10 2002

%E Extended by _Ray Chandler_, May 26 2008