A335278 First index of strictly decreasing prime quartets.

11, 18, 24, 47, 58, 62, 87, 91, 111, 114, 127, 132, 146, 150, 157, 180, 210, 223, 228, 232, 242, 259, 260, 263, 269, 274, 275, 282, 283, 284, 299, 300, 309, 321, 344, 350, 351, 363, 364, 367, 368, 369, 375, 378, 382, 388, 393, 399, 406, 409, 413, 431, 442, 446

Offset: 1

Author

Gus Wiseman, May 30 2020

Keywords

• nonn

Comments

Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k) > g(k + 1) > g(k + 2).

Examples

			The first 10 strictly decreasing prime quartets:
   31  37  41  43
   61  67  71  73
   89  97 101 103
  211 223 227 229
  271 277 281 283
  293 307 311 313
  449 457 461 463
  467 479 487 491
  607 613 617 619
  619 631 641 643
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.
		

Crossrefs

Prime gaps are A001223.

Second prime gaps are A036263.

Strictly increasing prime quartets are A335277.

Equal prime quartets are A090832.

Weakly increasing prime quartets are A333383.

Weakly decreasing prime quartets are A333488.

Unequal prime quartets are A333490.

Partially unequal prime quartets are A333491.

Positions of adjacent equal prime gaps are A064113.

Positions of strict ascents in prime gaps are A258025.

Positions of strict descents in prime gaps are A258026.

Positions of adjacent unequal prime gaps are A333214.

Positions of weak ascents in prime gaps are A333230.

Positions of weak descents in prime gaps are A333231.

Indices of strictly decreasing rows of A066099 are A333256.

Lengths of maximal weakly increasing sequences of prime gaps are A333215.

Lengths of maximal strictly decreasing sequences of prime gaps are A333252.

Cf. A000040, A006560, A031217, A054800, A054804, A059044, A084758, A089180, A333253.

Programs

Mathematica

ReplaceList[Array[Prime,100],{_,x_,y_,z_,t_,_}/;y-x>z-y>t-z:>PrimePi[x]]

Formula

prime(a(n)) = A054804(n).