cp's OEIS Frontend

A068019 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).

%I A068019 #20 Dec 08 2018 17:36:20
%S A068019 8,9,10,12,14,18,21,26,27,28,36,38,42,49,54,62,77,86,91,93,95,98,99,
%T A068019 111,117,122,124,133,135,146,148,152,154,171,182,186,189,190,198,206,
%U A068019 209,216,217,218,221,222,228,234,252,266,270,278,279,287,291,297,302
%N A068019 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 A068019 A072281 with the primes removed; intersection of A066071 and A078893. - _Ray Chandler_, May 26 2008
%H A068019 Michael De Vlieger, <a href="/A068019/b068019.txt">Table of n, a(n) for n = 1..10000</a>
%e A068019 n = 21, 26, 28, 36, 42 give phi(n)=12; the corresponding twin primes are {11,13}.
%t A068019 Do[s=-1+EulerPhi[n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]
%t A068019 (* Second program: *)
%t A068019 Select[Range[4, 302], And[CompositeQ@ #, AllTrue[EulerPhi@ # + {-1, 1}, PrimeQ]] &] (* _Michael De Vlieger_, Dec 08 2018 *)
%o A068019 (PARI) isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ _Michel Marcus_, Dec 08 2018
%o A068019 (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 A068019 Cf. A000010, A000040, A014574, A066071, A072281, A078893, A068017.
%K A068019 nonn
%O A068019 1,1
%A A068019 _Labos Elemer_, Feb 08 2002