A100965 Smallest prime number that ends a prime gap of at least 2n.

5, 11, 29, 97, 127, 127, 127, 541, 541, 907, 1151, 1361, 1361, 1361, 1361, 1361, 1361, 9587, 15727, 15727, 15727, 15727, 19661, 19661, 19661, 19661, 31469, 31469, 31469, 31469, 31469, 31469, 31469, 31469, 31469, 31469, 156007, 156007, 156007, 156007

Offset: 1

Author

T. D. Noe, Nov 23 2004

Keywords

• nonn

Comments

The second Mathematica program below generates the first 40 terms of the sequence given a value for nn of 15000. To generate the first 50 terms of the sequence the value of nn needs to be increased to about 32000. If a given value of nn is too low for the number of terms desired, this problem will be signaled by one or more of the generated terms being "NotFound" in which case increasing the value of nn appropriately should permit generating the desired number of terms. - Harvey P. Dale, Jul 10 2018

Examples

			a(5)=a(6)=a(7)=127 because there is a gap of 14 between 113 and 127.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A100964.

Programs

Mathematica

k=1; Table[While[Prime[k+1]-Prime[k] < 2n, k++ ]; Prime[k+1], {n, 48}]
Module[{nn=15000,pr,lst},pr=Prime[Range[2,nn]];lst=Thread[{pr,PadLeft[ Differences[ pr],nn-1]}];Table[SelectFirst[lst,#[[2]]>=2n&],{n,40}]][[All,1]] (* See Comment, above *) (* This program is several thousand times faster than the first program above *) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 08 2018 *)