A089038 Nonnegative numbers k such that 2k+5 is prime.

0, 1, 3, 4, 6, 7, 9, 12, 13, 16, 18, 19, 21, 24, 27, 28, 31, 33, 34, 37, 39, 42, 46, 48, 49, 51, 52, 54, 61, 63, 66, 67, 72, 73, 76, 79, 81, 84, 87, 88, 93, 94, 96, 97, 103, 109, 111, 112, 114, 117, 118, 123, 126, 129, 132, 133, 136, 138, 139, 144, 151, 153, 154, 156, 163

Offset: 1

Author

Ray Chandler, Nov 29 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086304.

Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), this seq (k=5), A105760 (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+5) ); # G. C. Greubel, May 21 2019

Magma

[n: n in [0..200]| IsPrime(2*n+5)]; // Vincenzo Librandi, Nov 17 2010

Mathematica

(Prime[Range[3,100]]-5)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[0, 200], PrimeQ[2*# + 5] &] (* Vincenzo Librandi, Oct 16 2012 *)

PARI

is(n)=isprime(2*n+5) \\ Charles R Greathouse IV, Feb 16 2017

Sage

[n for n in (0..200) if is_prime(2*n+5) ] # G. C. Greubel, May 21 2019

Formula

a(n) = (A086304(n-1) + 1)/2, n > 1.

Extensions

Removed wrong comment by Ralf Stephan, Nov 17 2010

Definition clarified by Zak Seidov, Jul 11 2014