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 A078872 #11 Jan 22 2022 00:07:25
%S A078872 11,17,41,29,59,5849,6959,599,149,3299,7,13,37,67,1597,19,4639,43,
%T A078872 17467,1601,23,2333,593,6353,1861,31,61,90001,32353,157,14731,47,587,
%U A078872 2671,3307,151,251,3301
%N A078872 The quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} are listed in lexicographic order; for each quintuple, this sequence lists the smallest prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5), if such a prime exists.
%C A078872 Comment from _N. J. A. Sloane_, Dec 04 2015: (Start)
%C A078872 The definition of A078872 is fairly subtle.
%C A078872 Step 1: The 3^5 = 243 quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} are listed in lexicographic order.
%C A078872 Step 2: Study each quintuple in turn. Look for the smallest prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5). If there is no such prime move on to next quintuple. If there is at least one such prime, take the smallest one, add it to the sequence, and move on to the next quintuple.
%C A078872 Each quintuple is considered just once, so there are at most 243 terms (in fact there are only 38).
%C A078872 (End)
%C A078872 The 38 quintuples for which p exists are listed, in decimal form, in A078870.
%e A078872 The term 67 corresponds to the quintuple (4,2,6,4,6): 67, 71, 73, 79, 83 and 89 are consecutive primes.
%Y A078872 The quintuples are in A078870. The same primes, in increasing order, are in A078873. The analogous sequences for quadruples and 6-tuples are in A078866 and A078874. Cf. A001223.
%K A078872 nonn,fini,full
%O A078872 1,1
%A A078872 _Labos Elemer_, Dec 20 2002
%E A078872 Edited by _Dean Hickerson_, Dec 21 2002