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A335277
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First index of strictly increasing prime quartets.
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3
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7, 13, 22, 28, 49, 60, 64, 69, 70, 75, 78, 85, 89, 95, 104, 116, 122, 123, 144, 148, 152, 155, 173, 178, 182, 195, 201, 206, 212, 215, 219, 225, 226, 230, 236, 237, 244, 253, 256, 257, 265, 288, 302, 307, 315, 325, 328, 329, 332, 333, 336, 348, 355, 361, 373
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OFFSET
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1,1
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COMMENTS
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Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k) < g(k + 1) < g(k + 2).
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LINKS
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FORMULA
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EXAMPLE
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The first 10 strictly increasing prime quartets:
17 19 23 29
41 43 47 53
79 83 89 97
107 109 113 127
227 229 233 239
281 283 293 307
311 313 317 331
347 349 353 359
349 353 359 367
379 383 389 397
For example, 107 is the 28th prime, and the primes (107,109,113,127) have differences (2,4,14), which are strictly increasing, so 28 is in the sequence.
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MATHEMATICA
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ReplaceList[Array[Prime, 100], {___, x_, y_, z_, t_, ___}/; y-x<z-y<t-z:>PrimePi[x]]
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CROSSREFS
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Strictly decreasing prime quartets are A335278.
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.
Lengths of maximal weakly decreasing sequences of prime gaps are A333212.
Lengths of maximal strictly increasing sequences of prime gaps are A333253.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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