A068081 - OEIS

%I #10 Sep 03 2017 21:54:26

%S 15,33,35,51,65,77,91,95,143,161,177,209,213,215,217,247,255,303,335,

%T 341,371,411,427,435,447,455,533,545,561,573,591,611,665,707,713,717,

%U 779,803,871,917,933,965,1001,1041,1067,1105,1115,1133,1157,1159,1211

%N Numbers n such that n + phi(n) and n - phi(n) are prime.

%H Harvey P. Dale, <a href="/A068081/b068081.txt">Table of n, a(n) for n = 1..1000</a>

%p with(numtheory): for n from 1 by 2 to 10^4 do if [isprime(n+phi(n)),

%p isprime(n-phi(n))]=[true,true] then print(n); fi; od; # _Muniru A Asiru_, Aug 31 2017

%t Select[ Range[1500], PrimeQ[ # + EulerPhi[ # ]] && PrimeQ[ # - EulerPhi[ # ]] & ]

%t epQ[n_]:=Module[{ep=EulerPhi[n]},AllTrue[n+{ep,-ep},PrimeQ]]; Select[ Range[ 1500],epQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 22 2016 *)

%o (PARI) is(n)=my(t=eulerphi(n)); isprime(n-t) && isprime(n+t) \\ _Charles R Greathouse IV_, Jan 25 2017

%o (GAP)

%o A068081:=[];; for n in [1,3..10^4+1] do if IsPrime(n+Phi(n)) and IsPrime(n-Phi(n)) then Add(A068081,n); fi; od; A068081;  # _Muniru A Asiru_, Aug 31 2017

%Y Cf. A050530, A068080.

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Feb 17 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 18 2002