%I #45 Feb 04 2024 01:19:34

%S 0,2,3,5,6,8,11,12,15,17,18,20,23,26,27,30,32,33,36,38,41,45,47,48,50,

%T 51,53,60,62,65,66,71,72,75,78,80,83,86,87,92,93,95,96,102,108,110,

%U 111,113,116,117,122,125,128,131,132,135,137,138,143,150,152,153,155,162

%N Nonnegative numbers k such that 2k+7 is prime.

%H Vincenzo Librandi, <a href="/A105760/b105760.txt">Table of n, a(n) for n = 1..1000</a>

%H Tony D. Noe and Jonathan Vos Post, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html">Primes in Fibonacci n-step and Lucas n-step Sequences,</a> J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.

%e If n=0, then 2*0 + 7 = 7 (prime).

%e If n=15, then 2*15 + 7 = 37 (prime).

%e If n=27, then 2*27 + 7 = 61 (prime).

%t (Prime[Range[4,100]]-7)/2 (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2010 *)

%t Select[Range[0, 200], PrimeQ[2 # + 7] &] (* _Vincenzo Librandi_, May 20 2014 *)

%o (Magma)[n: n in [0..200]| IsPrime(2*n+7)]; // _Vincenzo Librandi_, Dec 21 2010

%o (PARI) is(n)=isprime(2*n+7) \\ _Charles R Greathouse IV_, Feb 16 2017

%o (Sage) [n for n in (0..200) if is_prime(2*n+7) ] # _G. C. Greubel_, May 21 2019

%o (GAP) Filtered([0..200], k-> IsPrime(2*k+7) ) # _G. C. Greubel_, May 21 2019

%Y Cf. A153053 (Numbers n such that 2n+7 is not a prime)

%Y Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), this seq(k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).

%Y Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

%K easy,nonn

%O 1,2

%A _Parthasarathy Nambi_, May 04 2005

%E More terms from _Rick L. Shepherd_, May 18 2005