OFFSET
1,1
COMMENTS
In contrast with A015913, composite solutions are not rare. Prime solutions are common.
From Kevin J. Gomez, Mar 02 2016: (Start)
Composite solutions have two known forms:
n such that n = 4 * (2^p - 1) where 2^p - 1 is a Mersenne prime. (A001348)
n such that n = 8q where q is a Sophie Germain prime. (A005394)
There are composite solutions (such as 36) that do not fit either of these forms.
(End)
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
EXAMPLE
n=1048: phi(1048)=520, phi(1048+4)=524.
MATHEMATICA
Select[Range@1000, EulerPhi@(# + 4)== EulerPhi[#] + 4 &] (* Vincenzo Librandi, Sep 11 2015 *)
Position[Partition[EulerPhi[Range[1000]], 5, 1], _?(#[[1]]+4==#[[5]]&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Dec 18 2019 *)
PROG
(PARI) isok(n) = eulerphi(n+4) == eulerphi(n) + 4; \\ Michel Marcus, Sep 11 2015
(Magma) [n: n in [1..1000] | EulerPhi(n+4) eq EulerPhi(n)+4]; // Vincenzo Librandi, Sep 11 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 17 2000
STATUS
approved