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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A078892 A370090 A164374 * A242273 A261917 A111339

Adjacent sequences: A072278 A072279 A072280 * A072282 A072283 A072284

Keyword

easy,nonn

Author

Joseph L. Pe, Jul 10 2002

Extensions

Extended by Ray Chandler, May 26 2008

Status

approved