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 A050258 #39 Feb 16 2025 08:32:40
%S A050258 0,2,5,12,38,166,899,4768,28388,180529,1209318,8398278,60070590,
%T A050258 441296836,3314576487,25379433651,197622677481
%N A050258 Number of "prime quadruplets" with largest member < 10^n.
%C A050258 A "prime quadruplet" is a set of four primes {p, p+2, p+6, p+8}.
%C A050258 a(1) = 0 rather than 1 because the quadruple {2,3,5,7} does not have the official form.
%H A050258 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/quads/tabpi4.html">Enumeration of the prime quadruplets to 1e16</a>.
%H A050258 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/quads/quads.html">Enumeration to 1.6e15 of the prime quadruplets</a>.
%H A050258 Jonathan P. Sorenson, Jonathan Webster, <a href="https://arxiv.org/abs/1807.08777">Two Algorithms to Find Primes in Patterns</a>, arXiv:1807.08777 [math.NT], 2018.
%H A050258 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadruplet.html">Prime Quadruplet</a>.
%H A050258 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>.
%e A050258 a(2) = 2 because there are two prime quadruplets with largest member less than 10^2, namely {5, 7, 11, 13} and {11, 13, 17, 19}.
%e A050258 a(3) = 5 because, in addition to the prime quadruplets mentioned above, below 10^3 we also have {101, 103, 107, 109}, {191, 193, 197, 199} and {821, 823, 827, 829}.
%t A050258 c = 1; Do[ Do[ If[ PrimeQ[ n ] && PrimeQ[ n + 2 ] && PrimeQ[ n + 6 ] && PrimeQ[ n + 8 ], c++ ], {n, 10^n + 1, 10^(n + 1), 10} ]; Print[ c ], {n, 1, 15} ] (* Weisstein *)
%t A050258 (* First run program for A090258 *) Table[Length[Select[A090258, # < 10^n &]], {n, 5}] (* _Alonso del Arte_, Aug 12 2012 *)
%Y A050258 Cf. A007530.
%K A050258 nonn,nice,hard
%O A050258 1,2
%A A050258 _Eric W. Weisstein_
%E A050258 a(16) (from Nicely link) added by _Donovan Johnson_, Jan 11 2011
%E A050258 a(17) added by _Jonathan Webster_, Jun 26 2018
%E A050258 a(1) changed to 0 at the suggestion of _Harvey P. Dale_. - _N. J. A. Sloane_, Sep 25 2019