login
Numbers n such that n + 3 is prime.
2

%I #20 Sep 08 2022 08:45:40

%S 0,2,4,8,10,14,16,20,26,28,34,38,40,44,50,56,58,64,68,70,76,80,86,94,

%T 98,100,104,106,110,124,128,134,136,146,148,154,160,164,170,176,178,

%U 188,190,194,196,208,220,224,226,230,236,238,248,254,260,266,268,274,278

%N Numbers n such that n + 3 is prime.

%H G. C. Greubel, <a href="/A154115/b154115.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = A086801(n+1). - _R. J. Mathar_, May 09 2010

%e a(2) = 2 since (2 + 2)^2 - (2 + 1)^2 - 2 = 5.

%p A154115 := proc(n) ithprime(n+1)-3 ; end proc: # _R. J. Mathar_, May 09 2010

%t a[n_]:=(n+2)^2-(n+1)^2-n;lst={};Do[If[PrimeQ[a[n]],AppendTo[lst,n]],{n,6!}];lst

%t Select[Range[0,300],PrimeQ[(#+2)^2-(#+1)^2-#]&] (* _Harvey P. Dale_, Nov 06 2013 *)

%t Prime[Range[2,100]]-3 (* _Harvey P. Dale_, Jul 15 2017 *)

%o (Magma) [n: n in [0..500] | IsPrime((n+2)^2-(n+1)^2-n)] # _Vincenzo Librandi_, Nov 26 2010

%o (PARI) is(n)=isprime(n+3) \\ _Charles R Greathouse IV_, Sep 02 2016

%Y Cf. A140719, A005097, A154111, A154112, A154113.

%Y Cf. A067076 (a(n-1)/2).

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009

%E New name based on a comment by _Franklin T. Adams-Watters_, Jan 30 2009