A008995 Increasing length runs of consecutive composite numbers (endpoints).

4, 10, 28, 96, 126, 540, 906, 1150, 1360, 9586, 15726, 19660, 31468, 156006, 360748, 370372, 492226, 1349650, 1357332, 2010880, 4652506, 17051886, 20831532, 47326912, 122164968, 189695892, 191913030

Offset: 1

Author

Mark Cramer (m.cramer(AT)qut.edu.au). Computed by Dennis Yelle (dennis(AT)netcom.com)

Keywords

• nonn

References

• Netnews group rec.puzzles, circa Mar 01 1996 (I would like to get the exact reference).

Links

• MathForum rec.puzzles archive, Arithmetic Question 8 - consecutive.composites, June 2005.
• User "Abigail", 1000 consectutive composites (sic), post in newsgroup rec.puzzles, Jun 19 1996.
• Eric Weisstein's World of Mathematics, Prime Gaps.

Crossrefs

Cf. A000101, A008950, A008996.

Programs

Mathematica

maxGap = 1; Reap[ Do[ gap = Prime[n + 1] - (p = Prime[n]); If[gap > maxGap, Print[p + gap - 1]; Sow[p + gap - 1]; maxGap = gap], {n, 2, 10^8}]][[2, 1]] (* Jean-François Alcover, Jun 12 2013 *)

Formula

a(n) = A000101(n+1)-1.