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 A054808 #12 Oct 28 2018 09:10:34
%S A054808 1637,1759,1831,1847,1979,2357,2447,2477,2503,3413,3433,4177,4493,
%T A054808 5237,5399,5419,6011,6619,7219,7253,7727,7853,7907,8123,8467,9551,
%U A054808 9587,11003,11353,11551,11813,12379,13841,14797,15107,15511,16007,16273,16787,16993,17359,18149,18289
%N A054808 First term of strong prime quintets: p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3).
%C A054808 First member of pairs of consecutive primes in A054804 (first of strong quartets): The first 10^4 terms of that sequence yield over 2000 terms of this sequence. - _M. F. Hasler_, Oct 27 2018
%F A054808 a(n) = prevprime(A054809(n)); A054808 = {m = A054804(n) | nextprime(m) = A054804(n+1)}; nextprime = A151800, prevprime = A151799. - _M. F. Hasler_, Oct 27 2018
%t A054808 okQ[l_]:=Module[{d=Differences[l]},d[[1]]>d[[2]]>d[[3]]>d[[4]]]; Transpose[ Select[Partition[Prime[Range[2000]],5,1],okQ]][[1]] (* _Harvey P. Dale_, Aug 15 2011 *)
%o A054808 (PARI) A054808=List();for(i=2,1e4,A054804[i]==A054805[i-1]&&listput(A054808,A054804[i-1])) \\ _M. F. Hasler_, Oct 27 2018
%Y A054808 Cf. A051634, A051635; A054800 .. A054803: members of balanced prime quartets (= 4 consecutive primes in arithmetic progression); A054804 .. A054818: members of strong prime quartets, quintets, sextets; A054819 .. A054840: members of weak prime quartets, quintets, sextets, septets.
%K A054808 nonn
%O A054808 1,1
%A A054808 _Henry Bottomley_, Apr 10 2000
%E A054808 Edited and offset corrected to 1 by _M. F. Hasler_, Oct 27 2018