cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A054809 Second term of strong prime 5-tuples: p(m)-p(m-1) > p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2).

Original entry on oeis.org

1657, 1777, 1847, 1861, 1987, 2371, 2459, 2503, 2521, 3433, 3449, 4201, 4507, 5261, 5407, 5431, 6029, 6637, 7229, 7283, 7741, 7867, 7919, 8147, 8501, 9587, 9601, 11027, 11369, 11579, 11821, 12391, 13859, 14813, 15121, 15527, 16033, 16301, 16811, 17011, 17377
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Comments

Initial member of pairs of consecutive primes in A054805 (second of quadruples): The first 10^4 terms of that sequence yield over 2000 terms of this sequence. - M. F. Hasler, Oct 27 2018

Links

Crossrefs

Cf. A051634, A051635; A054800 .. A054803: members of balanced prime quadruples (= 4 consecutive primes in arithmetic progression); A054804 .. A054818: members of strong prime 4-tuples, 5-tuples, 6-tuples; A054819 .. A054840: members of weak prime 4-tuples, ..., 7-tuples.

Programs

  • Mathematica
    spqQ[n_]:=Module[{difs=Differences[n]},difs[[1]]>difs[[2]]> difs[[3]]> difs[[4]]]; Transpose[Select[Partition[Prime[ Range[2000]],5,1], spqQ]][[2]] (* Harvey P. Dale, May 06 2012 *)

Formula

a(n) = nextprime(A054808(n)) = prevprime(A054810(n)), nextprime = A151800, prevprime = A151799; A054809 = {m = A054805(n) | nextprime(m) = A054805(n+1)}. - M. F. Hasler, Oct 27 2018

Extensions

Corrected by Harvey P. Dale, May 06 2012
Edited and offset corrected to 1 by M. F. Hasler, Oct 27 2018

A054813 First term of strong prime sextets: p(m+1)-p(m) > p(m+2)-p(m+1) > p(m+3)-p(m+2) > p(m+4)-p(m+3) > p(m+5)-p(m+4).

Original entry on oeis.org

1831, 2477, 3413, 9551, 21433, 22973, 25189, 26053, 32143, 33359, 33893, 39047, 40771, 41203, 44221, 47251, 48787, 55849, 57751, 66977, 70079, 74231, 74653, 74687, 75083, 75109, 82913, 84263, 87811, 88339, 88609, 103723, 103843, 106219, 106921, 108139, 110881, 112979, 118093
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

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.

Formula

a(n) = A151799(A054814(n)), A054813 = { m = A054808(n) | m = A151799(A054808(n+1)) }, where A151799 = next smaller prime. - M. F. Hasler, Oct 27 2018

Extensions

More terms 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

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

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.

Programs

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

Formula

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

Extensions

Edited and offset changed to 1 by M. F. Hasler, Oct 26 2018
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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