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First term of strong prime quintets: p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3).
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%I #12 Oct 28 2018 09:10:34

%S 1637,1759,1831,1847,1979,2357,2447,2477,2503,3413,3433,4177,4493,

%T 5237,5399,5419,6011,6619,7219,7253,7727,7853,7907,8123,8467,9551,

%U 9587,11003,11353,11551,11813,12379,13841,14797,15107,15511,16007,16273,16787,16993,17359,18149,18289

%N First term of strong prime quintets: p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3).

%C First member of pairs of consecutive primes in A054804 (first of strong quartets): The first 10^4 terms of that sequence yield over 2000 terms of this sequence. - _M. F. Hasler_, Oct 27 2018

%F a(n) = prevprime(A054809(n)); A054808 = {m = A054804(n) | nextprime(m) = A054804(n+1)}; nextprime = A151800, prevprime = A151799. - _M. F. Hasler_, Oct 27 2018

%t okQ[l_]:=Module[{d=Differences[l]},d[[1]]>d[[2]]>d[[3]]>d[[4]]]; Transpose[ Select[Partition[Prime[Range[2000]],5,1],okQ]][[1]] (* _Harvey P. Dale_, Aug 15 2011 *)

%o (PARI) A054808=List();for(i=2,1e4,A054804[i]==A054805[i-1]&&listput(A054808,A054804[i-1])) \\ _M. F. Hasler_, Oct 27 2018

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

%K nonn

%O 1,1

%A _Henry Bottomley_, Apr 10 2000

%E Edited and offset corrected to 1 by _M. F. Hasler_, Oct 27 2018