

A333490


First index of unequal prime quartets.


9



7, 8, 10, 11, 13, 17, 18, 19, 20, 22, 23, 24, 28, 30, 31, 32, 34, 40, 42, 44, 47, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 75, 76, 78, 79, 82, 83, 85, 86, 87, 89, 90, 91, 94, 95, 96, 97, 98, 99, 104, 111, 112, 113, 114, 115, 116, 119
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OFFSET

1,1


COMMENTS

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.


LINKS



EXAMPLE

The first 10 unequal prime quartets:
17 19 23 29
19 23 29 31
29 31 37 41
31 37 41 43
41 43 47 53
59 61 67 71
61 67 71 73
67 71 73 79
71 73 79 83
79 83 89 97
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.


MATHEMATICA

ReplaceList[Array[Prime, 100], {___, x_, y_, z_, t_, ___}/; yx!=zy!=tz:>PrimePi[x]]


CROSSREFS

Lengths of maximal antirun subsequences of prime gaps are A333216.
Lengths of maximal runs of prime gaps are A333254.
Maximal antiruns in standard compositions are counted by A333381.
Strictly decreasing prime quartets are A054804.
Strictly increasing prime quartets are A054819.
Weakly increasing prime quartets are A333383.
Weakly decreasing prime quartets are A333488.
Unequal prime quartets are A333490 (this sequence).
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.


KEYWORD

nonn


AUTHOR



STATUS

approved



