A054809 -id:A054809 - cp's OEIS frontend

A054808 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).

1637, 1759, 1831, 1847, 1979, 2357, 2447, 2477, 2503, 3413, 3433, 4177, 4493, 5237, 5399, 5419, 6011, 6619, 7219, 7253, 7727, 7853, 7907, 8123, 8467, 9551, 9587, 11003, 11353, 11551, 11813, 12379, 13841, 14797, 15107, 15511, 16007, 16273, 16787, 16993, 17359, 18149, 18289

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

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

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.

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 *)

A054808=List();for(i=2,1e4,A054804[i]==A054805[i-1]&&listput(A054808,A054804[i-1])) \\ M. F. Hasler, Oct 27 2018

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

Edited and offset corrected to 1 by M. F. Hasler, Oct 27 2018

A054814 Second term p(m) of strong prime sextets: p(m)-p(m-1) > p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3).

Original entry on oeis.org

1847, 2503, 3433, 9587, 21467, 22993, 25219, 26083, 32159, 33377, 33911, 39079, 40787, 41213, 44249, 47269, 48799, 55871, 57773, 67003, 70099, 74257, 74687, 74699, 75109, 75133, 82939, 84299, 87833, 88379, 88643, 103769, 103867, 106243, 106937, 108161, 110899, 112997, 118127, 120371

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

M. F. Hasler, Table of n, a(n) for n = 1..2500, Oct 27 2018

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

Subsequence of A054808.

Select[Partition[Prime[Range[12000]],6,1],Max[Differences[#,2]]<0&][[;;,2]] (* Harvey P. Dale, Jun 17 2023 *)

a(n) = A151800(A054813(n)) = A151799(A054815(n)), A151800 = nextprime, A151799 = prevprime; A054814 = { m = A054809(n) | m = nextprime(A054809(n-1)) }. - M. F. Hasler, Oct 27 2018

Edited and offset changed to 1 by M. F. Hasler, Oct 26 2018

cp's OEIS Frontend

A054808 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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