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A335278 First index of strictly decreasing prime quartets.

%I A335278 #5 May 30 2020 19:14:48
%S A335278 11,18,24,47,58,62,87,91,111,114,127,132,146,150,157,180,210,223,228,
%T A335278 232,242,259,260,263,269,274,275,282,283,284,299,300,309,321,344,350,
%U A335278 351,363,364,367,368,369,375,378,382,388,393,399,406,409,413,431,442,446
%N A335278 First index of strictly decreasing prime quartets.
%C A335278 Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k) > g(k + 1) > g(k + 2).
%F A335278 prime(a(n)) = A054804(n).
%e A335278 The first 10 strictly decreasing prime quartets:
%e A335278    31  37  41  43
%e A335278    61  67  71  73
%e A335278    89  97 101 103
%e A335278   211 223 227 229
%e A335278   271 277 281 283
%e A335278   293 307 311 313
%e A335278   449 457 461 463
%e A335278   467 479 487 491
%e A335278   607 613 617 619
%e A335278   619 631 641 643
%e A335278 For example, 211 is the 47th prime, and the primes (211,223,227,229) have differences (12,4,2), which are strictly decreasing, so 47 is in the sequence.
%t A335278 ReplaceList[Array[Prime,100],{___,x_,y_,z_,t_,___}/;y-x>z-y>t-z:>PrimePi[x]]
%Y A335278 Prime gaps are A001223.
%Y A335278 Second prime gaps are A036263.
%Y A335278 Strictly increasing prime quartets are A335277.
%Y A335278 Equal prime quartets are A090832.
%Y A335278 Weakly increasing prime quartets are A333383.
%Y A335278 Weakly decreasing prime quartets are A333488.
%Y A335278 Unequal prime quartets are A333490.
%Y A335278 Partially unequal prime quartets are A333491.
%Y A335278 Positions of adjacent equal prime gaps are A064113.
%Y A335278 Positions of strict ascents in prime gaps are A258025.
%Y A335278 Positions of strict descents in prime gaps are A258026.
%Y A335278 Positions of adjacent unequal prime gaps are A333214.
%Y A335278 Positions of weak ascents in prime gaps are A333230.
%Y A335278 Positions of weak descents in prime gaps are A333231.
%Y A335278 Indices of strictly decreasing rows of A066099 are A333256.
%Y A335278 Lengths of maximal weakly increasing sequences of prime gaps are A333215.
%Y A335278 Lengths of maximal strictly decreasing sequences of prime gaps are A333252.
%Y A335278 Cf. A000040, A006560, A031217, A054800, A054804, A059044, A084758, A089180, A333253.
%K A335278 nonn
%O A335278 1,1
%A A335278 _Gus Wiseman_, May 30 2020