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 A259488 #37 Feb 18 2018 14:58:29 %S A259488 2,3,7,13,296,343,395,405,408,463,469,473,542,572,577,584,625,671,673, %T A259488 695,837,984,1016,1030,1074,1165,1224,1230,1328,1410,1445,1679,1825, %U A259488 1860,1867,1949,2078,2091,2095,2123,2167,2476,2478,2616,2753,2764,2956,3011,3065,3416,3621,3646,3712,3720,3758,3872,3926,4063,4071,4079,4133,4217,4312,4351,4524,4745,4855,4865,4882,4922 %N A259488 Positive integers k with prime(k)+2 and prime(prime(k))+2 both prime. %C A259488 The conjecture in A259487 essentially says that {a(m)/a(n): m,n = 1,2,3,...} coincides with the set of all positive rational numbers. This implies that the current sequence has infinitely many terms. %D A259488 Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187. %H A259488 Zhi-Wei Sun, <a href="/A259488/b259488.txt">Table of n, a(n) for n = 1..10000</a> %H A259488 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014. %e A259488 a(1) = 2 since prime(2)+2 = 5 and prime(prime(2))+2 = prime(3)+2 = 7 are both prime, but prime(1)+2 = 4 is composite. %e A259488 a(2) = 3 since prime(3)+2 = 7 and prime(prime(3))+2 = prime(7)+2 = 19 are both prime. %t A259488 n=0;Do[If[PrimeQ[Prime[k]+2]&&PrimeQ[Prime[Prime[k]]+2],n=n+1;Print[n," ",k]],{k,1,5000}] %t A259488 Select[Range[5000],AllTrue[{Prime[#]+2,Prime[Prime[#]]+2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 18 2018 *) %o A259488 (PARI) k=pk=0; forprime(ppk=2,1e6, if(isprime(pk++),k++; if(isprime(pk+2) && isprime(ppk+2), print1(k", ")))) \\ _Charles R Greathouse IV_, Jun 29 2015 %Y A259488 Cf. A000040, A001359, A006512, A236458, A236470, A259487. %K A259488 nonn %O A259488 1,1 %A A259488 _Zhi-Wei Sun_, Jun 28 2015