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 A333490 #5 May 16 2020 14:28:42
%S A333490 7,8,10,11,13,17,18,19,20,22,23,24,28,30,31,32,34,40,42,44,47,49,50,
%T A333490 51,52,57,58,59,60,61,62,64,65,66,67,68,69,70,75,76,78,79,82,83,85,86,
%U A333490 87,89,90,91,94,95,96,97,98,99,104,111,112,113,114,115,116,119
%N A333490 First index of unequal prime quartets.
%C A333490 Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k), g(k + 1), and g(k + 2) are all different.
%e A333490 The first 10 unequal prime quartets:
%e A333490 17 19 23 29
%e A333490 19 23 29 31
%e A333490 29 31 37 41
%e A333490 31 37 41 43
%e A333490 41 43 47 53
%e A333490 59 61 67 71
%e A333490 61 67 71 73
%e A333490 67 71 73 79
%e A333490 71 73 79 83
%e A333490 79 83 89 97
%e A333490 For example, 83 is the 23rd prime, and the primes (83,89,97,101) have differences (6,8,4), which are all distinct, so 23 is in the sequence.
%t A333490 ReplaceList[Array[Prime,100],{___,x_,y_,z_,t_,___}/;y-x!=z-y!=t-z:>PrimePi[x]]
%Y A333490 Primes are A000040.
%Y A333490 Prime gaps are A001223.
%Y A333490 Second prime gaps are A036263.
%Y A333490 Indices of unequal rows of A066099 are A233564.
%Y A333490 Lengths of maximal anti-run subsequences of prime gaps are A333216.
%Y A333490 Lengths of maximal runs of prime gaps are A333254.
%Y A333490 Maximal anti-runs in standard compositions are counted by A333381.
%Y A333490 Indices of anti-run rows of A066099 are A333489.
%Y A333490 Strictly decreasing prime quartets are A054804.
%Y A333490 Strictly increasing prime quartets are A054819.
%Y A333490 Equal prime quartets are A090832.
%Y A333490 Weakly increasing prime quartets are A333383.
%Y A333490 Weakly decreasing prime quartets are A333488.
%Y A333490 Unequal prime quartets are A333490 (this sequence).
%Y A333490 Partially unequal prime quartets are A333491.
%Y A333490 Positions of adjacent equal prime gaps are A064113.
%Y A333490 Positions of strict ascents in prime gaps are A258025.
%Y A333490 Positions of strict descents in prime gaps are A258026.
%Y A333490 Positions of adjacent unequal prime gaps are A333214.
%Y A333490 Positions of weak ascents in prime gaps are A333230.
%Y A333490 Positions of weak descents in prime gaps are A333231.
%Y A333490 Cf. A006560, A031217, A054800, A059044, A084758, A089180, A124767, A333215.
%K A333490 nonn
%O A333490 1,1
%A A333490 _Gus Wiseman_, May 15 2020