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%I #12 Aug 28 2021 12:21:25
%S 41,71,101,227,281,311,461,487,617,641,727,757,857,881,937,1091,1301,
%T 1427,1451,1481,1549,1663,1667,1697,1741,1783,1787,1861,1867,1871,
%U 1993,1997,2063,2141,2339,2377,2381,2467,2473,2521,2531,2539,2591,2617,2657
%N Third term of strong prime quartets: prime(m+1)-prime(m) > prime(m+2)-prime(m+1) > prime(m+3)-prime(m+2).
%H M. F. Hasler, <a href="/A054806/b054806.txt">Table of n, a(n) for n = 1..10000</a>, Oct 27 2018
%F a(n) = nextprime(A054805(n)) = prevprime(A054807(n)), nextprime = A151800, prevprime = A151799. - _M. F. Hasler_, Oct 27 2018
%t Select[Partition[Prime[Range[400]],4,1],Max[Differences[#,2]]<0&][[All,3]] (* _Harvey P. Dale_, Aug 28 2021 *)
%Y 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.
%K nonn
%O 1,1
%A _Henry Bottomley_, Apr 10 2000
%E Offset corrected to 1 by _M. F. Hasler_, Oct 27 2018
%E Definition clarified by _N. J. A. Sloane_, Aug 28 2021
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