A054819 First term of weak prime quartet: p(m+1)-p(m) < p(m+2)-p(m+1) < p(m+3)-p(m+2).

17, 41, 79, 107, 227, 281, 311, 347, 349, 379, 397, 439, 461, 499, 569, 641, 673, 677, 827, 857, 881, 907, 1031, 1061, 1091, 1187, 1229, 1277, 1301, 1319, 1367, 1427, 1429, 1451, 1487, 1489, 1549, 1607, 1619, 1621, 1697, 1877, 1997, 2027, 2087, 2153

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = prime(A335277(n)). - Gus Wiseman, May 31 2020

Example

From Gus Wiseman, May 31 2020: (Start)
The first 10 strictly increasing prime gap 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
(End)

Mathematica

wpqQ[lst_]:=Module[{diffs=Differences[lst]}, diffs[[1]]<diffs[[2]]<diffs[[3]]]; Transpose[Select[Partition[Prime[ Range[400]], 4, 1], wpqQ]][[1]] (* Harvey P. Dale, Jun 12 2012 *)
ReplaceList[Array[Prime, 100], {___, x_, y_, z_, t_, ___}/; y-x<z-y<t-z:>x] (* Gus Wiseman, May 31 2020 *)

Crossrefs

Cf. A051635, A054800-A054840.

Prime gaps are A001223.

Second prime gaps are A036263.

Strictly decreasing prime gap quartets are A335278.

Strictly increasing prime gap quartets are A335277.

Equal prime gap quartets are A090832.

Weakly increasing prime gap quartets are A333383.

Weakly decreasing prime gap quartets are A333488.

Unequal prime gap quartets are A333490.

Partially unequal prime gap 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.

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

Sequence in context: A028886 A146443 A110226 * A235743 A299797 A087877

Adjacent sequences: A054816 A054817 A054818 * A054820 A054821 A054822

Keyword

nonn

Author

Henry Bottomley, Apr 10 2000

Status

approved