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URL: https://oeis.org/A072281

⇱ A072281 - OEIS

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A072281
Numbers n such that phi(n) + 1 and phi(n) - 1 are twin primes.
10
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
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
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Jul 10 2002
EXTENSIONS
Extended by Ray Chandler, May 26 2008
STATUS
approved