%I #40 Feb 03 2024 00:51:37
%S 0,2,3,5,8,9,12,14,15,17,20,23,24,27,29,30,33,35,38,42,44,45,47,48,50,
%T 57,59,62,63,68,69,72,75,77,80,83,84,89,90,92,93,99,105,107,108,110,
%U 113,114,119,122,125,128,129,132,134,135,140,147,149,150,152,159,162,167
%N Nonnegative numbers k such that 2k + 13 is prime.
%C Or, (p-13)/2 for primes p >= 13.
%C a(n) = (A000040(n+5) - 13)/2.
%C a(n) = A005097(n+4) - 6.
%C a(n) = A067076(n+4) - 5.
%C a(n) = A089038(n+3) - 4.
%C a(n) = A105760(n+2) - 3.
%C a(n) = A101448(n+1) - 1.
%C a(n) = A089559(n-1) + 1 for n > 1.
%H Vincenzo Librandi, <a href="/A153081/b153081.txt">Table of n, a(n) for n = 1..1000</a>
%e For k = 7, 2*k+13 = 27 is not prime, so 7 is not in the sequence;
%e for k = 8, 2*k+13 = 29 is prime, so 8 is in the sequence.
%t (Prime[Range[6,100]]-13)/2 (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2010 *)
%t Select[Range[0,200],PrimeQ[2#+13]&] (* _Harvey P. Dale_, Mar 02 2015 *)
%o (Magma) [ n: n in [0..200] | IsPrime(2*n+13) ];
%o (PARI) is(n)=isprime(2*n+13) \\ _Charles R Greathouse IV_, Jul 12 2016
%o (Sage) [n for n in (0..200) if is_prime(2*n+13) ] # _G. C. Greubel_, May 22 2019
%o (GAP) Filtered([0..200], k-> IsPrime(2*k+13) ) # _G. C. Greubel_, May 22 2019
%Y Cf. A000040 (prime numbers).
%Y 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), this seq (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
%Y 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 easy,nonn
%O 1,2
%A _Vincenzo Librandi_, Dec 18 2008
%E Edited and extended by _Klaus Brockhaus_, Dec 22 2008
%E Definition clarified by _Zak Seidov_, Jul 11 2014
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