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A333491 First index of partially unequal prime quartets. 9
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 37, 40, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let g(i) = prime(i + 1) - prime(i). These are numbers k such that g(k) != g(k + 1) != g(k + 2), but we may have g(k) = g(k + 2).

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

The first 10 partially unequal prime quartets:

   5  7 11 13

   7 11 13 17

  11 13 17 19

  13 17 19 23

  17 19 23 29

  19 23 29 31

  23 29 31 37

  29 31 37 41

  31 37 41 43

  37 41 43 47

MATHEMATICA

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

CROSSREFS

Primes are A000040.

Prime gaps are A001223.

Second prime gaps are A036263.

Indices of unequal rows of A066099 are A233564.

Lengths of maximal anti-runs of prime gaps are A333216.

Lengths of maximal runs of prime gaps are A333254.

Maximal anti-runs in standard compositions are counted by A333381.

Indices of anti-run rows of A066099 are A333489.

Strictly decreasing prime quartets are A054804.

Strictly increasing prime quartets are A054819.

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 (this sequence).

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.

Cf. A006560, A031217, A054800, A059044, A084758, A089180, A124767, A333215.

Sequence in context: A194378 A283810 A130231 * A304816 A298005 A216442

Adjacent sequences:  A333488 A333489 A333490 * A333492 A333493 A333494

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 15 2020

STATUS

approved

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)