A051635 -id:A051635 - cp's OEIS frontend

A054826 Fourth term of weak prime quintets: p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m).

359, 691, 1439, 1499, 1637, 2221, 2251, 2699, 2927, 2939, 4111, 4139, 4943, 5591, 5953, 6287, 6491, 6719, 6841, 8101, 8191, 8243, 8951, 10343, 10753, 11789, 12119, 12301, 13487, 13499, 13913, 13921, 14107, 14639, 14683, 14969, 14983, 15091

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Cf. A051635, A054800-A054840.

Transpose[Select[Partition[Prime[Range[2000]],5,1],Min[ Differences[ #,2]]>0&]] [[4]] (* Harvey P. Dale, May 07 2015 *)

A054829 Second term of weak prime sextet: 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

2909, 13469, 13903, 14951, 15377, 15383, 21401, 21559, 21863, 28279, 30871, 33203, 35593, 37693, 42223, 42571, 45823, 55663, 64663, 64921, 64927, 68209, 68213, 68899, 68903, 73943, 74203, 78583, 83093, 85517, 87317, 88003, 90911

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

a(1) = A229832(4). - Jonathan Sondow, Oct 13 2013

Cf. A051635, A054800-A054840, A229832.

wps[{a_,b_,c_,d_,e_,f_}]:=b-aHarvey P. Dale, Jun 25 2013 *)

A054831 Fourth term of weak prime sextet: 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

2927, 13487, 13913, 14969, 15391, 15401, 21419, 21569, 21881, 28289, 30893, 33223, 35603, 37717, 42239, 42589, 45833, 55673, 64679, 64937, 64951, 68219, 68227, 68909, 68917, 73961, 74219, 78607, 83117, 85531, 87337, 88019, 90931

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A051635, A054800-A054840.

Select[Partition[Prime[Range[9000]],6,1],Min[Differences[#,2]]>0&][[All,4]] (* Harvey P. Dale, Sep 18 2022 *)

A054833 Sixth term of weak prime sextet: 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

2953, 13513, 13931, 15013, 15413, 15427, 21467, 21587, 21911, 28307, 30931, 33287, 35671, 37781, 42281, 42641, 45853, 55691, 64709, 64969, 64997, 68239, 68261, 68927, 68947, 73999, 74257, 78643, 83177, 85571, 87383, 88069, 90971, 91621, 92297, 97073, 106853, 118529, 119083, 127807, 129011

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Transpose[Select[Partition[Prime[Range[9000]],6,1],And@@Positive[ Differences[ #,2]]&]][[6]] (* Harvey P. Dale, Nov 06 2011 *)

a(n) = A151800(A054832(n)). - M. F. Hasler, Oct 27 2018

A054834 First term of weak prime septet: 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) < p(m+6)-p(m+5).

Original entry on oeis.org

15373, 64919, 68207, 68897, 128981, 128983, 143509, 154079, 157999, 192373, 221717, 222379, 244457, 249721, 285287, 318677, 337277, 354371, 357823, 374173, 385391, 394727, 402581, 402583, 419597, 439157, 441907, 448373, 457397, 457669, 458189, 482507, 527981, 529811, 577529, 582761, 655909

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

M. F. Hasler, Table of n, a(n) for n = 1..1000, Oct 27 2018
Shyam Sunder Gupta, Elegance of Squares, Cubes, and Higher Powers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 2, 29-81.

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.

Select[Partition[Prime[Range[54000]],7,1],Min[Differences[#,2]]>0&][[All,1]] (* Harvey P. Dale, Mar 16 2020 *)

a(n) = A151799(A054835(n)), A151799 = prevprime; A054834 = { m = A054828(n) | m = prevprime(A054828(n+1)) }. - M. F. Hasler, Oct 27 2018

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

A054837 Fourth term of weak prime septet: 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) < p(m+3)-p(m+2).

Original entry on oeis.org

15391, 64937, 68219, 68909, 128993, 129001, 143527, 154097, 158017, 192391, 221729, 222419, 244481, 249749, 285317, 318691, 337291, 354383, 357859, 374203, 385403, 394739, 402593, 402601, 419609, 439183, 441937, 448397, 457411, 457687, 458207, 482519, 527993

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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.

Transpose[Select[Partition[Prime[Range[100000]],7,1],Min[ Differences[ #,2]] > 0&]][[4]] (* Harvey P. Dale, Aug 29 2013 *)

a(n) = A151800(A054836(n)) = A151799(A054838(n)), A151800 = nextprime, A151799 = prevprime; A054837 = { m = A054830(n) | m = nextprime(A054830(n-1)) }. - M. F. Hasler, Oct 27 2018

More terms from Harvey P. Dale, Aug 29 2013

A155188 Sophie Germain primes that are also strong primes and lesser of twin prime pairs.

Original entry on oeis.org

11, 29, 41, 179, 191, 239, 281, 419, 431, 641, 659, 809, 1019, 1031, 1049, 1229, 1289, 1451, 1481, 1931, 2129, 2141, 2339, 2549, 2969, 3299, 3329, 3359, 3389, 3539, 3821, 3851, 4019, 4271, 4481, 5231, 5279, 5441, 5501, 5639, 5741, 5849, 6131, 6269, 6449

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A045536, A005384, A051634, A006562, A051635.

lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];If[p1>(p0+p2)/2,If[PrimeQ[p1*2+1],If[PrimeQ[p1+2],AppendTo[lst,p1]]]],{n,7!}];lst

A054820 Second term of weak prime quartet: p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).

Original entry on oeis.org

19, 43, 83, 109, 229, 283, 313, 349, 353, 383, 401, 443, 463, 503, 571, 643, 677, 683, 829, 859, 883, 911, 1033, 1063, 1093, 1193, 1231, 1279, 1303, 1321, 1373, 1429, 1433, 1453, 1489, 1493, 1553, 1609, 1621, 1627, 1699, 1879, 1999, 2029, 2089, 2161

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Lesser of a pair p(m), p(m+1) of consecutive weak primes A051635. See A229832 for more comments, references and links. - Jonathan Sondow, Oct 13 2013

a(1) = A229832(2). - Jonathan Sondow, Oct 13 2013

Cf. A051635, A054800-A054840, A229832.

A054825 Third term of weak prime quintets: 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

353, 683, 1433, 1493, 1627, 2213, 2243, 2693, 2917, 2927, 4099, 4133, 4937, 5581, 5939, 6277, 6481, 6709, 6833, 8093, 8179, 8237, 8941, 10337, 10739, 11783, 12113, 12289, 13477, 13487, 13907, 13913, 14087, 14633, 14669, 14957, 14969, 15083

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A051635, A054800-A054840.

Select[Partition[Prime[Range[2000]], 5, 1], Min[Differences[ #, 2]] > 0 &] [[All, 3]](* Harvey P. Dale, Jul 09 2017 *)

A054827 Fifth term of weak prime quintets: 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

367, 701, 1447, 1511, 1657, 2237, 2267, 2707, 2939, 2953, 4127, 4153, 4951, 5623, 5981, 6299, 6521, 6733, 6857, 8111, 8209, 8263, 8963, 10357, 10771, 11801, 12143, 12323, 13499, 13513, 13921, 13931, 14143, 14653, 14699, 14983, 15013, 15101, 15401, 15413, 15427, 16411, 17417, 17957, 18287, 19373, 19949

Offset: 1

Henry Bottomley, Apr 10 2000

nonn

M. F. Hasler, Table of n, a(n) for n = 1..10000

Cf. A051635, A054800-A054840.

a(n) = A151800(A054826(n)). - M. F. Hasler, Oct 26 2018

More terms from M. F. Hasler, Oct 26 2018

cp's OEIS Frontend

A054826 Fourth term of weak prime quintets: p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m).

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A054829 Second term of weak prime sextet: 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).

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A054831 Fourth term of weak prime sextet: 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).

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A054833 Sixth term of weak prime sextet: 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).

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A054834 First term of weak prime septet: 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) < p(m+6)-p(m+5).

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A054837 Fourth term of weak prime septet: 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) < p(m+3)-p(m+2).

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A155188 Sophie Germain primes that are also strong primes and lesser of twin prime pairs.

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A054820 Second term of weak prime quartet: p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).

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A054825 Third term of weak prime quintets: p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m) < p(m+2)-p(m+1).

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A054827 Fifth term of weak prime quintets: p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1).

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