A072281 Numbers n such that phi(n) + 1 and phi(n) - 1 are twin primes.

5, 7, 8, 9, 10, 12, 13, 14, 18, 19, 21, 26, 27, 28, 31, 36, 38, 42, 43, 49, 54, 61, 62, 73, 77, 86, 91, 93, 95, 98, 99, 103, 109, 111, 117, 122, 124, 133, 135, 139, 146, 148, 151, 152, 154, 171, 181, 182, 186, 189, 190, 193, 198, 199, 206, 209, 216, 217, 218, 221, 222

Offset: 1

Author

Joseph L. Pe, Jul 10 2002

Keywords

• easy
• nonn

Comments

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

The positions of isolated nonprimes in A000010. - Juri-Stepan Gerasimov, Nov 10 2009

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Select[Range[10^3], PrimeQ[EulerPhi[ # ] + 1] && PrimeQ[EulerPhi[ # ] - 1] &]
Select[Range[300],And@@PrimeQ[EulerPhi[#]+{1,-1}]&] (* Harvey P. Dale, Apr 07 2012 *)

PARI

isok(n) = my(p); isprime(p=eulerphi(n)-1) && isprime(p+2); \\ Michel Marcus, Sep 29 2019

Extensions

Extended by Ray Chandler, May 26 2008