A054807 Fourth term of strong prime quartets: prime(m+1)-prime(m) > prime(m+2)-prime(m+1) > prime(m+3)-prime(m+2).

43, 73, 103, 229, 283, 313, 463, 491, 619, 643, 733, 761, 859, 883, 941, 1093, 1303, 1429, 1453, 1483, 1553, 1667, 1669, 1699, 1747, 1787, 1789, 1867, 1871, 1873, 1997, 1999, 2069, 2143, 2341, 2381, 2383, 2473, 2477, 2531, 2539, 2543, 2593, 2621, 2659

Offset

1,1

Links

M. F. Hasler, Table of n, a(n) for n = 1..10000, Oct 27 2018

Formula

a(n) = nextprime(A054806(n)), nextprime = A151800. - M. F. Hasler, Oct 27 2018

Mathematica

Select[Partition[Prime[Range[400]], 4, 1], Max[Differences[#, 2]]<0&][[;; , 4]] (* Harvey P. Dale, Dec 25 2025 *)

Crossrefs

Cf. A051634, A051635; A054800 .. A054803: members of balanced prime quartets (= 4 consecutive primes in arithmetic progression); A054804 .. A054818: members of strong prime quartet, quintet, sextet; A054819 .. A054840: members of weak prime quartet, quintet, sextet, septets.

Sequence in context: A144974 A144975 A087699 * A394750 A285017 A139932

Adjacent sequences: A054804 A054805 A054806 * A054808 A054809 A054810

Keyword

nonn

Author

Henry Bottomley, Apr 10 2000

Extensions

Offset corrected to 1 by M. F. Hasler, Oct 27 2018

Definition clarified by N. J. A. Sloane, Aug 28 2021.

Status

approved