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).

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

Author

Henry Bottomley, Apr 10 2000

Keywords

• nonn

Links

• 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.

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

Formula

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

Extensions

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