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

Author

Vincenzo Librandi, Dec 19 2008

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

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).

Programs

GAP

Filtered([0..200], k-> IsPrime(2*k+19) ); # G. C. Greubel, May 22 2019

Magma

[ n: n in [0..165] | IsPrime(2*n+19) ];

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 *)

PARI

is(n)=isprime(2*n+19) \\ Charles R Greathouse IV, Feb 17 2017

PARI

list(lim)=apply(p->p\2-9, primes([19,lim\1*2+19])) \\ Charles R Greathouse IV, Jan 03 2025

Sage

[n for n in (0..200) if is_prime(2*n+19) ] # G. C. Greubel, May 22 2019

Formula

a(n) ~ (n/2) log n. - Charles R Greathouse IV, Jan 03 2025

Extensions

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

Definition clarified by Zak Seidov, Jul 11 2014