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A054819 First term of weak prime quartet: p(m+1)-p(m) < p(m+2)-p(m+1) < p(m+3)-p(m+2).

%I A054819 #13 Jun 19 2020 03:58:36
%S A054819 17,41,79,107,227,281,311,347,349,379,397,439,461,499,569,641,673,677,
%T A054819 827,857,881,907,1031,1061,1091,1187,1229,1277,1301,1319,1367,1427,
%U A054819 1429,1451,1487,1489,1549,1607,1619,1621,1697,1877,1997,2027,2087,2153
%N A054819 First term of weak prime quartet: p(m+1)-p(m) < p(m+2)-p(m+1) < p(m+3)-p(m+2).
%H A054819 Harvey P. Dale, <a href="/A054819/b054819.txt">Table of n, a(n) for n = 1..1000</a>
%F A054819 a(n) = prime(A335277(n)). - _Gus Wiseman_, May 31 2020
%e A054819 From _Gus Wiseman_, May 31 2020: (Start)
%e A054819 The first 10 strictly increasing prime gap quartets:
%e A054819    17   19   23   29
%e A054819    41   43   47   53
%e A054819    79   83   89   97
%e A054819   107  109  113  127
%e A054819   227  229  233  239
%e A054819   281  283  293  307
%e A054819   311  313  317  331
%e A054819   347  349  353  359
%e A054819   349  353  359  367
%e A054819   379  383  389  397
%e A054819 (End)
%t A054819 wpqQ[lst_]:=Module[{diffs=Differences[lst]},diffs[[1]]<diffs[[2]]<diffs[[3]]]; Transpose[Select[Partition[Prime[ Range[400]], 4,1],wpqQ]][[1]] (* _Harvey P. Dale_, Jun 12 2012 *)
%t A054819 ReplaceList[Array[Prime,100],{___,x_,y_,z_,t_,___}/;y-x<z-y<t-z:>x] (* _Gus Wiseman_, May 31 2020 *)
%Y A054819 Cf. A051635, A054800-A054840.
%Y A054819 Prime gaps are A001223.
%Y A054819 Second prime gaps are A036263.
%Y A054819 Strictly decreasing prime gap quartets are A335278.
%Y A054819 Strictly increasing prime gap quartets are A335277.
%Y A054819 Equal prime gap quartets are A090832.
%Y A054819 Weakly increasing prime gap quartets are A333383.
%Y A054819 Weakly decreasing prime gap quartets are A333488.
%Y A054819 Unequal prime gap quartets are A333490.
%Y A054819 Partially unequal prime gap quartets are A333491.
%Y A054819 Positions of adjacent equal prime gaps are A064113.
%Y A054819 Positions of strict ascents in prime gaps are A258025.
%Y A054819 Positions of strict descents in prime gaps are A258026.
%Y A054819 Positions of adjacent unequal prime gaps are A333214.
%Y A054819 Positions of weak ascents in prime gaps are A333230.
%Y A054819 Positions of weak descents in prime gaps are A333231.
%Y A054819 Lengths of maximal weakly decreasing sequences of prime gaps are A333212.
%Y A054819 Lengths of maximal strictly increasing sequences of prime gaps are A333253.
%Y A054819 Cf. A000040, A006560, A031217, A059044, A084758, A089180, A333253.
%K A054819 nonn
%O A054819 1,1
%A A054819 _Henry Bottomley_, Apr 10 2000