A153081 Nonnegative numbers k such that 2k + 13 is prime.

0, 2, 3, 5, 8, 9, 12, 14, 15, 17, 20, 23, 24, 27, 29, 30, 33, 35, 38, 42, 44, 45, 47, 48, 50, 57, 59, 62, 63, 68, 69, 72, 75, 77, 80, 83, 84, 89, 90, 92, 93, 99, 105, 107, 108, 110, 113, 114, 119, 122, 125, 128, 129, 132, 134, 135, 140, 147, 149, 150, 152, 159, 162, 167

Offset: 1

Author

Vincenzo Librandi, Dec 18 2008

Keywords

• easy
• nonn

Comments

Or, (p-13)/2 for primes p >= 13.

a(n) = (A000040(n+5) - 13)/2.

a(n) = A005097(n+4) - 6.

a(n) = A067076(n+4) - 5.

a(n) = A089038(n+3) - 4.

a(n) = A105760(n+2) - 3.

a(n) = A101448(n+1) - 1.

a(n) = A089559(n-1) + 1 for n > 1.

Examples

			For k = 7, 2*k+13 = 27 is not prime, so 7 is not in the sequence;
for k = 8, 2*k+13 = 29 is prime, so 8 is in the sequence.
		

Links

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

Crossrefs

Cf. A000040 (prime numbers).

Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), this seq (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+13) ); # G. C. Greubel, May 22 2019

Magma

[ n: n in [0..200] | IsPrime(2*n+13) ];

Mathematica

(Prime[Range[6,100]]-13)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[0,200],PrimeQ[2#+13]&] (* Harvey P. Dale, Mar 02 2015 *)

PARI

is(n)=isprime(2*n+13) \\ Charles R Greathouse IV, Jul 12 2016

Sage

[n for n in (0..200) if is_prime(2*n+13) ] # G. C. Greubel, May 22 2019

Extensions

Edited and extended by Klaus Brockhaus, Dec 22 2008

Definition clarified by Zak Seidov, Jul 11 2014