OFFSET
1,1
COMMENTS
The majority of solutions can be predicted by known properties of the equality. There are several solutions that do not fit these parameters.
A natural number n is a solution if either:
n and n + 6 are both prime (sexy primes) (A023201);
n = 2^k*p with k>0 and p prime, such that 2^k*(p+1) - 1 is also prime.
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10000
Wikipedia, Euler's totient function
EXAMPLE
5 is a term since phi(5+6) = 10 = 6 + 4 = phi(5) + 6.
MATHEMATICA
Select[Range@500, EulerPhi@(# + 6)== EulerPhi[#] + 6 &] (* Vincenzo Librandi, Sep 11 2015 *)
PROG
(Sage) [n for n in [1..1000] if euler_phi(n+6)==euler_phi(n)+6] # Tom Edgar, Sep 10 2015
(Magma) [n: n in [1..500] | EulerPhi(n+6) eq EulerPhi(n)+6]; // Vincenzo Librandi, Sep 11 2015
(PARI) is(n)=eulerphi(n + 6) == eulerphi(n) + 6 \\ Anders Hellström, Sep 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kevin J. Gomez, Sep 10 2015
STATUS
approved