A105760 Nonnegative numbers k such that 2k+7 is prime.

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, 51, 53, 60, 62, 65, 66, 71, 72, 75, 78, 80, 83, 86, 87, 92, 93, 95, 96, 102, 108, 110, 111, 113, 116, 117, 122, 125, 128, 131, 132, 135, 137, 138, 143, 150, 152, 153, 155, 162

Offset: 1

Author

Parthasarathy Nambi, May 04 2005

Keywords

• easy
• nonn

Examples

			If n=0, then 2*0 + 7 = 7 (prime).
If n=15, then 2*15 + 7 = 37 (prime).
If n=27, then 2*27 + 7 = 61 (prime).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.

Crossrefs

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

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).

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).

Programs

GAP

Filtered([0..200], k-> IsPrime(2*k+7) ); # G. C. Greubel, May 21 2019

Magma

[n: n in [0..200]| IsPrime(2*n+7)]; // Vincenzo Librandi, Dec 21 2010

Mathematica

(Prime[Range[4,100]]-7)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[0, 200], PrimeQ[2 # + 7] &] (* Vincenzo Librandi, May 20 2014 *)

PARI

is(n)=isprime(2*n+7) \\ Charles R Greathouse IV, Feb 16 2017

Sage

[n for n in (0..200) if is_prime(2*n+7) ] # G. C. Greubel, May 21 2019

Extensions

More terms from Rick L. Shepherd, May 18 2005