A153143 Nonnegative numbers k such that 2k + 19 is prime.

0, 2, 5, 6, 9, 11, 12, 14, 17, 20, 21, 24, 26, 27, 30, 32, 35, 39, 41, 42, 44, 45, 47, 54, 56, 59, 60, 65, 66, 69, 72, 74, 77, 80, 81, 86, 87, 89, 90, 96, 102, 104, 105, 107, 110, 111, 116, 119, 122, 125, 126, 129, 131, 132, 137, 144, 146, 147, 149, 156, 159, 164, 165

Offset

1,2

Comments

Or, (p-19)/2 for primes p >= 19.

a(n) = (A000040(n+7) - 19)/2.

a(n) = A005097(n+6) - 9.

a(n) = A067076(n+6) - 8.

a(n) = A089038(n+5) - 7.

a(n) = A105760(n+4) - 6.

a(n) = A101448(n+3) - 4.

a(n) = A089559(n+1) - 2.

Links

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

Example

For k = 4, 2*k+19 = 27 is not prime, so 4 is not in the sequence;
for k = 17, 2*k+19 = 53 is prime, so 17 is in the sequence.

Mathematica

(Prime[Range[8, 100]]-19)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[0, 170], PrimeQ[(2*#)+19]&] (* Vincenzo Librandi, Sep 24 2012 *)

Prog

(Magma) [ n: n in [0..165] | IsPrime(2*n+19) ];
(PARI) is(n)=isprime(2*n+19) \\ Charles R Greathouse IV, Feb 17 2017
(Sage) [n for n in (0..200) if is_prime(2*n+19) ] # G. C. Greubel, May 22 2019
(GAP) Filtered([0..200], k-> IsPrime(2*k+19) ) # G. C. Greubel, May 22 2019

Crossrefs

Cf. A000040 (prime numbers), A153144 (2n+19 is not prime).

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), A153081 (k=13), A089559 (k=15), A173059 (k=17), this seq (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).

Sequence in context: A166087 A333545 A281902 * A075724 A049408 A342733

Adjacent sequences: A153140 A153141 A153142 * A153144 A153145 A153146

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 19 2008

Extensions

Edited, corrected and extended by Klaus Brockhaus, Dec 22 2008

Definition clarified by Zak Seidov, Jul 11 2014

Status

approved