A068081 Numbers n such that n + phi(n) and n - phi(n) are prime.

15, 33, 35, 51, 65, 77, 91, 95, 143, 161, 177, 209, 213, 215, 217, 247, 255, 303, 335, 341, 371, 411, 427, 435, 447, 455, 533, 545, 561, 573, 591, 611, 665, 707, 713, 717, 779, 803, 871, 917, 933, 965, 1001, 1041, 1067, 1105, 1115, 1133, 1157, 1159, 1211

Offset: 1

Author

Amarnath Murthy, Feb 17 2002

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A050530, A068080.

Programs

GAP

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

Maple

with(numtheory): for n from 1 by 2 to 10^4 do if [isprime(n+phi(n)),
isprime(n-phi(n))]=[true,true] then print(n); fi; od; # Muniru A Asiru, Aug 31 2017

Mathematica

Select[ Range[1500], PrimeQ[ # + EulerPhi[ # ]] && PrimeQ[ # - EulerPhi[ # ]] & ]
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 *)

PARI

is(n)=my(t=eulerphi(n)); isprime(n-t) && isprime(n+t) \\ Charles R Greathouse IV, Jan 25 2017

Extensions

Edited and extended by Robert G. Wilson v, Feb 18 2002