A217724 Smallest prime producing a gap with the next prime, the size of the gap being a composite number with 2n+1 as a factor.

139, 1831, 1129, 2971, 1327, 19333, 81463, 19609, 44293, 89689, 173359, 212701, 265621, 544279, 1100977, 396733, 1098847, 370261, 1349533, 6752623, 5518687, 6371401, 10343761, 2010733, 4652353, 33803689, 83751121, 38394127, 39389989, 79167733, 142414669

Offset

1,1

Comments

The "gap" is defined as the number of integers between two primes. If the two primes are p1 and p2, then the size of the gap is p2-p1-1.

For at least n<=100, the gap is minimal and is 3*(2n+1).

Links

Robert Price, Table of n, a(n) for n = 1..100

Example

For n=2, the required gap is a composite number with 5 (2n+1) as a factor.  The size of all gaps are odd, so gaps of 15, 25, 35, etc. are required.  The prime 1831 and its next prime of 1847 produces a gap of 15.  1831 is the smallest prime with this property.

Crossrefs

Cf. A067836.

Sequence in context: A358400 A175017 A271977 * A230693 A223163 A158527

Adjacent sequences: A217721 A217722 A217723 * A217725 A217726 A217727

Keyword

nonn

Author

Robert Price, Mar 21 2013

Status

approved