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Composite n such that both 1 + phi(n) and -1 + phi(n) are primes, i.e., phi(n) is the middle term between twin primes (A014574).
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%I #20 Dec 08 2018 17:36:20

%S 8,9,10,12,14,18,21,26,27,28,36,38,42,49,54,62,77,86,91,93,95,98,99,

%T 111,117,122,124,133,135,146,148,152,154,171,182,186,189,190,198,206,

%U 209,216,217,218,221,222,228,234,252,266,270,278,279,287,291,297,302

%N Composite n such that both 1 + phi(n) and -1 + phi(n) are primes, i.e., phi(n) is the middle term between twin primes (A014574).

%C A072281 with the primes removed; intersection of A066071 and A078893. - _Ray Chandler_, May 26 2008

%H Michael De Vlieger, <a href="/A068019/b068019.txt">Table of n, a(n) for n = 1..10000</a>

%e n = 21, 26, 28, 36, 42 give phi(n)=12; the corresponding twin primes are {11,13}.

%t Do[s=-1+EulerPhi[n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]

%t (* Second program: *)

%t Select[Range[4, 302], And[CompositeQ@ #, AllTrue[EulerPhi@ # + {-1, 1}, PrimeQ]] &] (* _Michael De Vlieger_, Dec 08 2018 *)

%o (PARI) isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ _Michel Marcus_, Dec 08 2018

%o (GAP) Filtered([1..310],n->not IsPrime(n) and IsPrime(1+Phi(n)) and IsPrime(-1+Phi(n))); # _Muniru A Asiru_, Dec 08 2018

%Y Cf. A000010, A000040, A014574, A066071, A072281, A078893, A068017.

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 08 2002