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A153143 Nonnegative numbers k such that 2k + 19 is prime. 25
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 (list; graph; refs; listen; history; text; internal format)
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
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
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

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Last modified July 20 15:12 EDT 2024. Contains 374459 sequences. (Running on oeis4.)