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 A007693 M0656 #54 Mar 27 2025 05:20:57 %S A007693 2,3,5,7,11,13,17,23,37,47,61,73,83,101,103,107,131,137,151,173,181, %T A007693 233,241,257,263,271,277,283,293,311,313,331,347,367,373,397,443,461, %U A007693 467,503,557,577,593,601,607,641,653,661,683,727,751,761,773,787,797,853 %N A007693 Primes p such that 6*p + 1 is also prime. %D A007693 Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 83. %D A007693 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A007693 Amiram Eldar, <a href="/A007693/b007693.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale) %H A007693 Andrew Granville, <a href="http://dx.doi.org/10.1016/0022-314X(87)90052-7">Sophie Germain's theorem for prime pairs p, 6p+1</a>, J. Number Theory 27 (1987), no. 1, 63-72. %F A007693 a(n) = (A051644(n)-1)/6. %t A007693 Select[Prime@Range[150], PrimeQ[6# + 1] &] (* _Ray Chandler_, Mar 14 2007 *) %o A007693 (Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(6*n+1)]; // _Vincenzo Librandi_, Nov 18 2010 %o A007693 (PARI) isok(k) = isprime(k) && isprime(6*k+1); \\ _Amiram Eldar_, Feb 24 2025 %Y A007693 Cf. A002476, A016921, A024899, A051644, A091178, A023256 (subset: 6*(6p+1)+1 also prime). %Y A007693 Prime terms of A024899. %K A007693 nonn,easy %O A007693 1,1 %A A007693 _N. J. A. Sloane_ and _Robert G. Wilson v_ %E A007693 Extended by _Ray Chandler_, Mar 14 2007