OFFSET
1,1
COMMENTS
Below 100000 no common composite solutions with sigma(n+2)=sigma(n)+2, while prime solutions are common.
phi(x)+2=phi(x+2) is equivalent to cototient(x+2)=cototient(x), so also defines closest numbers with identical value of cototients (A051953), either primes or composites.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
n=254, phi(254+2) = phi(256) = 128 = phi(254)+2 = 126+2.
MATHEMATICA
Select[Range[5000], CompositeQ[#]&&EulerPhi[#]+2==EulerPhi[#+2]&] (* Harvey P. Dale, Jul 10 2017 *)
PROG
(PARI) isok(n) = !isprime(n) && (eulerphi(n+2) == eulerphi(n)+2); \\ Michel Marcus, Aug 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 17 2000
STATUS
approved