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 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

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