login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153143 Nonnegative numbers n such that 2n + 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.

Solutions of the equation (2*n+19)' = 1, where n' is the arithmetic derivative of n. - Paolo P. Lava, Nov 15 2012

LINKS

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

EXAMPLE

For n = 4, 2*n+19 = 27 is not prime, so 4 is not in the sequence; for n = 17, 2*n+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: A244749 A166087 A281902 * A075724 A049408 A138970

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 02:56 EDT 2019. Contains 325290 sequences. (Running on oeis4.)