A068019 - OEIS

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).

8, 9, 10, 12, 14, 18, 21, 26, 27, 28, 36, 38, 42, 49, 54, 62, 77, 86, 91, 93, 95, 98, 99, 111, 117, 122, 124, 133, 135, 146, 148, 152, 154, 171, 182, 186, 189, 190, 198, 206, 209, 216, 217, 218, 221, 222, 228, 234, 252, 266, 270, 278, 279, 287, 291, 297, 302

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A072281 with the primes removed; intersection of A066071 and A078893. - Ray Chandler, May 26 2008

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

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

MATHEMATICA

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

(* Second program: *)

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

PROG

(PARI) isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ Michel Marcus, Dec 08 2018

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

CROSSREFS

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

Sequence in context: A024884 A031009 A120184 * A054011 A280946 A209724

Adjacent sequences: A068016 A068017 A068018 * A068020 A068021 A068022

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 08 2002

STATUS

approved