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 1-10 of 18 results. Next

A054840 Seventh term of weak prime septet: p(m-5)-p(m-6) < p(m-4)-p(m-5) < p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1).

Original entry on oeis.org

15427, 64997, 68261, 68947, 129023, 129037, 143567, 154153, 158071, 192461, 221773, 222493, 244529, 249797, 285421, 318737, 337327, 354421, 357967, 374287, 385471, 394787, 402631, 402691, 419687, 439253, 442003, 448519, 457459, 457739, 458309, 482569, 528041, 529927, 577589, 582809
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

Cf. 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.

Programs

  • Mathematica
    Select[Partition[Prime[Range[50000]],7,1],Min[Differences[#,2]]>0&][[;;,7]] (* Harvey P. Dale, Aug 25 2024 *)

Formula

a(n) = nextprime(A054839), nextprime = A151800;
A054840 = { A054833(n) | A054833(n) = nextprime(A054833(n-1)) }. - M. F. Hasler, Oct 27 2018

Extensions

Edited and more terms from M. F. Hasler, Oct 27 2018

A054805 Second term of strong prime quartets: prime(m+1)-prime(m) > prime(m+2)-prime(m+1) > prime(m+3)-prime(m+2).

Original entry on oeis.org

37, 67, 97, 223, 277, 307, 457, 479, 613, 631, 719, 751, 853, 877, 929, 1087, 1297, 1423, 1447, 1471, 1543, 1657, 1663, 1693, 1733, 1777, 1783, 1847, 1861, 1867, 1987, 1993, 2053, 2137, 2333, 2371, 2377, 2459, 2467, 2503, 2521, 2531, 2579, 2609, 2647
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Comments

Second member of pairs of consecutive primes in A051634 (strong primes). - M. F. Hasler, Oct 27 2018

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) = nextprime(A054804(n))= prevprime(A054806(n)), nextprime = A151800, prevprime = A151799. - M. F. Hasler, Oct 27 2018

Extensions

Offset corrected to 1 by M. F. Hasler, Oct 27 2018
Definition clarified by N. J. A. Sloane, Aug 28 2021

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

Original entry on oeis.org

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

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

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.

Formula

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

Extensions

Offset corrected to 1 by M. F. Hasler, Oct 27 2018
Definition clarified by N. J. A. Sloane, Aug 28 2021.

A054806 Third term of strong prime quartets: prime(m+1)-prime(m) > prime(m+2)-prime(m+1) > prime(m+3)-prime(m+2).

Original entry on oeis.org

41, 71, 101, 227, 281, 311, 461, 487, 617, 641, 727, 757, 857, 881, 937, 1091, 1301, 1427, 1451, 1481, 1549, 1663, 1667, 1697, 1741, 1783, 1787, 1861, 1867, 1871, 1993, 1997, 2063, 2141, 2339, 2377, 2381, 2467, 2473, 2521, 2531, 2539, 2591, 2617, 2657
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

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.

Programs

  • Mathematica
    Select[Partition[Prime[Range[400]],4,1],Max[Differences[#,2]]<0&][[All,3]] (* Harvey P. Dale, Aug 28 2021 *)

Formula

a(n) = nextprime(A054805(n)) = prevprime(A054807(n)), nextprime = A151800, prevprime = A151799. - M. F. Hasler, Oct 27 2018

Extensions

Offset corrected to 1 by M. F. Hasler, Oct 27 2018
Definition clarified by N. J. A. Sloane, Aug 28 2021

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).

Original entry on oeis.org

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

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Comments

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

Crossrefs

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.

Programs

Formula

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

Extensions

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

A054835 Second term of weak prime septet: 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) < p(m+5)-p(m+4).

Original entry on oeis.org

15377, 64921, 68209, 68899, 128983, 128987, 143513, 154081, 158003, 192377, 221719, 222389, 244463, 249727, 285289, 318679, 337279, 354373, 357829, 374177, 385393, 394729, 402583, 402587, 419599, 439163, 441913, 448379, 457399, 457673, 458191, 482509, 527983, 529813, 577531, 582763, 655913
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

Cf. A051635, A229832.
Cf. 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(1) = A229832(5). - Jonathan Sondow, Oct 13 2013
a(n) = A151800(A054834(n)) = A151799(A054836(n)), A151800 = nextprime, A151799 = prevprime; A054835 = { m = A054828(n) | m = nextprime(A054828(n-1)) }. - M. F. Hasler, Oct 27 2018

Extensions

More terms from M. F. Hasler, Oct 27 2018

A054838 Fifth term of weak prime septet: p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).

Original entry on oeis.org

15401, 64951, 68227, 68917, 129001, 129011, 143537, 154111, 158029, 192407, 221737, 222437, 244493, 249763, 285343, 318701, 337301, 354391, 357883, 374219, 385417, 394747, 402601, 402613, 419623, 439199, 441953, 448421, 457421, 457697, 458219, 482527, 528001
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

Cf. 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.

Programs

  • Mathematica
    Select[Partition[Prime[Range[7000]],7,1],Min[Differences[#,2]]>0&][[All,5]] (* Harvey P. Dale, Oct 15 2016 *)

Formula

a(n) = A151800(A054837(n)) = A151799(A054839(n)), A151800 = nextprime, A151799 = prevprime; A054838 = { m = A054831(n) | m = nextprime(A054831(n-1)) }. - M. F. Hasler, Oct 27 2018

Extensions

More terms from Harvey P. Dale, Oct 15 2016

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

A054810 Third term of strong prime 5-tuples: p(m-1)-p(m-2) > p(m)-p(m-1) > p(m+1)-p(m) > p(m+2)-p(m+1).

Original entry on oeis.org

1663, 1783, 1861, 1867, 1993, 2377, 2467, 2521, 2531, 3449, 3457, 4211, 4513, 5273, 5413, 5437, 6037, 6653, 7237, 7297, 7753, 7873, 7927, 8161, 8513, 9601, 9613, 11047, 11383, 11587, 11827, 12401, 13873, 14821, 15131, 15541, 16057, 16319
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

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[{a_,b_,c_,d_,e_}]:=(b-a)>(c-b)>(d-c)>(e-d); Transpose[ Select[ Partition[ Prime[ Range[2000]],5,1],spqQ]][[3]] (* Harvey P. Dale, Feb 25 2013 *)

Extensions

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

A054836 Third term of weak prime septet: p(m-1)-p(m-2) < 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

15383, 64927, 68213, 68903, 128987, 128993, 143519, 154087, 158009, 192383, 221723, 222403, 244471, 249737, 285301, 318683, 337283, 354377, 357839, 374189, 385397, 394733, 402587, 402593, 419603, 439171, 441923, 448387, 457403, 457679, 458197, 482513, 527987, 529819, 577537, 582767
Offset: 1

Views

Author

Henry Bottomley, Apr 10 2000

Keywords

Links

Crossrefs

Cf. 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.

Formula

a(n) = A151800(A054835(n)) = A151799(A054838(n)), A151800 = nextprime, A151799 = prevprime; A054836 = { m = A054829(n) | m = nextprime(A054829(n-1)) }. - M. F. Hasler, Oct 27 2018

Extensions

More terms from M. F. Hasler, Oct 27 2018
Showing 1-10 of 18 results. Next

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