A111871 Prime gaps q-p with n-th record merit referred to in A111870.

1, 2, 4, 14, 22, 34, 52, 72, 86, 96, 112, 132, 148, 180, 210, 248, 282, 320, 336, 354, 382, 456, 514, 532, 582, 588, 602, 652, 716, 766, 906, 1132, 1328, 1356, 1370, 1442, 1476, 1572

Offset: 1

Author

N. J. A. Sloane, based on correspondence with Ed Pegg Jr, Nov 23 2005

Keywords

• nonn
• hard
• more

Comments

The prime gaps q-p (corresponding to a(n)=p in A111870) have increasing record merit (q-p)/log(p). However, the prime gaps themselves are almost always monotonically increasing (with very high probability), but not always! And we do have an exception in the list above: a(14)=148 < a(13)=154! (But see next comment!)

Because the erroneous A111870(13) = 4652353 term was removed, a(13) = 154 was removed. This sequence is therefore monotonically increasing. - John W. Nicholson, Nov 18 2013

Examples

			A111870(4) = 113 and the next larger prime is 127, so 127 - A111870(4) = a(4) = 14.
		

References

• Ed Pegg, Jr., Posting to Seq Fan mailing list, Nov 23, 2005

Links

• Jens Kruse Andersen, Norman Luhn, Record prime gaps.

Crossrefs

For the primes p corresponding to the prime gaps q-p with n-th record merit, see A111870.

Cf. A002386, A277552.

Formula

a(n) = A277552(n) - A111870(n). - Bobby Jacobs, Nov 13 2016

Extensions

Corrected and edited by Daniel Forgues, Nov 11 2009 and Nov 20 2009

Because the erroneous A111870(13) = 4652353 term was removed, a(13) = 154 was removed by John W. Nicholson, Nov 18 2013

a(33)-a(35) inserted by Bobby Jacobs, Nov 08 2016

a(37) added by Bobby Jacobs, Nov 09 2016

a(38) added by Rodolfo Ruiz-Huidobro, May 14 2024