This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063908 #60 Sep 08 2022 08:45:04
%S A063908 3,5,7,11,13,17,23,31,37,41,43,53,67,71,83,97,101,107,113,127,137,157,
%T A063908 167,181,191,193,211,223,233,241,251,263,283,311,317,331,347,373,421,
%U A063908 431,433,443,457,461,487,521,547,563,577,587,613,617,631,641,643,647
%N A063908 Numbers k such that k and 2*k-3 are primes.
%C A063908 If p is in this sequence then the products of positive powers of 3, p and 2p-3 are entries in A086486. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003
%C A063908 Median prime of AP3's starting at 3, i.e., triples of primes (3,p,q) in arithmetic progression. - _M. F. Hasler_, Sep 24 2009
%C A063908 a(n) = sum of the coprimes(p) mod (p+1). - _J. M. Bergot_, Nov 13 2014
%C A063908 A010051(2*a(n)-3) = 1. - _Reinhard Zumkeller_, Jul 02 2015
%C A063908 A098090 INTERSECT A000040. - _R. J. Mathar_, Mar 23 2017
%H A063908 Harry J. Smith and K. D. Bajpai, <a href="/A063908/b063908.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%H A063908 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_034.htm">Puzzle 34.- Prime Triplets in arithmetic progression</a>, The Prime Puzzles & Problems Connection. [From _M. F. Hasler_, Sep 24 2009]
%F A063908 a(n) = A241817(n)/2. - _Wesley Ivan Hurt_, Apr 08 2018
%e A063908 From _K. D. Bajpai_, Nov 29 2019: (Start)
%e A063908 a(5) = 13 is prime and 2*13 - 3 = 23 is also prime.
%e A063908 a(6) = 17 is prime and 2*17 - 3 = 31 is also prime.
%e A063908 (End)
%p A063908 select(k -> andmap(isprime, [k, 2*k-3]), [seq(k, k=1.. 10^4)]); # _K. D. Bajpai_, Nov 29 2019
%t A063908 Select[Prime[Range[6! ]],PrimeQ[2*#-3]&] (* _Vladimir Joseph Stephan Orlovsky_, Nov 17 2009 *)
%o A063908 (PARI) { n=0; p=1; for (m=1, 10^9, p=nextprime(p+1); if (isprime(2*p - 3), write("b063908.txt", n++, " ", p); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 02 2009
%o A063908 (PARI) forprime( p=1,default(primelimit), isprime(2*p-3) && print1(p",")) \\ _M. F. Hasler_, Sep 24 2009
%o A063908 (Magma) [n : n in [0..700] | IsPrime(n) and IsPrime(2*n-3)]; // _Vincenzo Librandi_, Nov 14 2014
%o A063908 (Haskell)
%o A063908 a063908 n = a063908_list !! (n-1)
%o A063908 a063908_list = filter
%o A063908 ((== 1) . a010051' . (subtract 3) . (* 2)) a000040_list
%o A063908 -- _Reinhard Zumkeller_, Jul 02 2015
%Y A063908 Cf. A005382.
%Y A063908 Cf. A000040, A010051, A088878, A172287.
%Y A063908 Cf. A259730.
%K A063908 nonn
%O A063908 1,1
%A A063908 _N. J. A. Sloane_, Aug 31 2001