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

%I A153143 #47 Jan 03 2025 22:56:35
%S A153143 0,2,5,6,9,11,12,14,17,20,21,24,26,27,30,32,35,39,41,42,44,45,47,54,
%T A153143 56,59,60,65,66,69,72,74,77,80,81,86,87,89,90,96,102,104,105,107,110,
%U A153143 111,116,119,122,125,126,129,131,132,137,144,146,147,149,156,159,164,165
%N A153143 Nonnegative numbers k such that 2k + 19 is prime.
%C A153143 Or, (p-19)/2 for primes p >= 19.
%C A153143 a(n) = (A000040(n+7) - 19)/2.
%C A153143 a(n) = A005097(n+6) - 9.
%C A153143 a(n) = A067076(n+6) - 8.
%C A153143 a(n) = A089038(n+5) - 7.
%C A153143 a(n) = A105760(n+4) - 6.
%C A153143 a(n) = A101448(n+3) - 4.
%C A153143 a(n) = A089559(n+1) - 2.
%H A153143 Vincenzo Librandi, <a href="/A153143/b153143.txt">Table of n, a(n) for n = 1..1000</a>
%F A153143 a(n) ~ (n/2) log n. - _Charles R Greathouse IV_, Jan 03 2025
%e A153143 For k = 4, 2*k+19 = 27 is not prime, so 4 is not in the sequence;
%e A153143 for k = 17, 2*k+19 = 53 is prime, so 17 is in the sequence.
%t A153143 (Prime[Range[8,100]]-19)/2 (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2010 *)
%t A153143 Select[Range[0, 170], PrimeQ[(2*#)+19]&] (* _Vincenzo Librandi_, Sep 24 2012 *)
%o A153143 (Magma) [ n: n in [0..165] | IsPrime(2*n+19) ];
%o A153143 (PARI) is(n)=isprime(2*n+19) \\ _Charles R Greathouse IV_, Feb 17 2017
%o A153143 (PARI) list(lim)=apply(p->p\2-9, primes([19,lim\1*2+19])) \\ _Charles R Greathouse IV_, Jan 03 2025
%o A153143 (Sage) [n for n in (0..200) if is_prime(2*n+19) ] # _G. C. Greubel_, May 22 2019
%o A153143 (GAP) Filtered([0..200], k-> IsPrime(2*k+19) ); # _G. C. Greubel_, May 22 2019
%Y A153143 Cf. A000040 (prime numbers), A153144 (2n+19 is not prime).
%Y A153143 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).
%Y A153143 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).
%K A153143 nonn,easy
%O A153143 1,2
%A A153143 _Vincenzo Librandi_, Dec 19 2008
%E A153143 Edited, corrected and extended by _Klaus Brockhaus_, Dec 22 2008
%E A153143 Definition clarified by _Zak Seidov_, Jul 11 2014