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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.
1
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
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
KEYWORD
nonn
AUTHOR
Robert Price, Mar 21 2013
STATUS
approved