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 A078870 #12 Mar 25 2017 20:28:26
%S A078870 24246,24626,24662,26424,26426,26462,26466,26642,26646,26664,42424,
%T A078870 42462,42466,42646,46246,46264,46266,46626,46662,62462,62642,62646,
%U A078870 62664,62666,64242,64246,64264,64624,64626,64662,64666,66264,66266,66424,66462,66466,66626,66646
%N A078870 Decimal concatenations of the 38 quintuples (d1,d2,d3,d4,d5) with elements in {2,4,6} for which there exists a prime p >= 7 such that the differences between the 6 consecutive primes starting with p are (d1,d2,d3,d4,d5).
%e A078870 66646 is in the sequence because 3301, 3307, 3313, 3319, 3323 and 3329 are consecutive primes with differences (6,6,6,4,6).
%t A078870 With[{k = 5}, FromDigits /@ Select[Tuples[Range[2, 6, 2], k], Function[m, Count[Range[k - 1, 10^4], n_ /; Times @@ Boole@ Map[PrimeQ, Prime@ n + Accumulate@ m] == 1] > 0]]] (* _Michael De Vlieger_, Mar 25 2017 *) (* or *)
%t A078870 FromDigits /@ Union@ Select[ Partition[ Differences@ Prime[Range[4, 9000]], 5, 1], Max@ # <= 6 &] (* _Giovanni Resta_, Mar 25 2017 *)
%Y A078870 Cf. A078868, A078869.
%K A078870 fini,full,base,nonn
%O A078870 1,1
%A A078870 _Labos Elemer_, Dec 19 2002
%E A078870 Edited by _Dean Hickerson_, Dec 20 2002